5441:
888:
5217:
4533:
5130:
5313:
1303:
901:
77:
4518:
5340:
174:
4386:
5102:, may have been the first to maintain the idea that "everything happens for a reason" and that theoretical principles can assist in the understanding of nature. While to a modern reader, many of these preserved ideas come forth as eminently reasonable, there is a conspicuous lack of both mathematical
2364:
accelerate in relation to another inertial frame. A body rotating with respect to an inertial frame is not an inertial frame. When viewed from an inertial frame, particles in the non-inertial frame appear to move in ways not explained by forces from existing fields in the reference frame. Hence, it
1138:
Another division is based on the choice of mathematical formalism. Classical mechanics can be mathematically presented in multiple different ways. The physical content of these different formulations is the same, but they provide different insights and facilitate different types of calculations.
3890:
5266:. The combination of Newton's laws of motion and gravitation provides the fullest and most accurate description of classical mechanics. He demonstrated that these laws apply to everyday objects as well as to celestial objects. In particular, he obtained a theoretical explanation of
3715:
2282:
2839:
3998:
2916:
So long as the force acting on a particle is known, Newton's second law is sufficient to describe the motion of a particle. Once independent relations for each force acting on a particle are available, they can be substituted into Newton's second law to obtain an
5327:
After Newton, classical mechanics became a principal field of study in mathematics as well as physics. Mathematical formulations progressively allowed finding solutions to a far greater number of problems. The first notable mathematical treatment was in 1788 by
2329:. An inertial frame is an idealized frame of reference within which an object with zero net force acting upon it moves with a constant velocity; that is, it is either at rest or moving uniformly in a straight line. In an inertial frame Newton's law of motion,
1884:
In classical mechanics, velocities are directly additive and subtractive. For example, if one car travels east at 60 km/h and passes another car traveling in the same direction at 50 km/h, the slower car perceives the faster car as traveling east at
2587:
4513:{\displaystyle {\frac {\mathrm {d} {\boldsymbol {q}}}{\mathrm {d} t}}={\frac {\partial {\mathcal {H}}}{\partial {\boldsymbol {p}}}},\quad {\frac {\mathrm {d} {\boldsymbol {p}}}{\mathrm {d} t}}=-{\frac {\partial {\mathcal {H}}}{\partial {\boldsymbol {q}}}}.}
4563:(QFT) is of use. QFT deals with small distances, and large speeds with many degrees of freedom as well as the possibility of any change in the number of particles throughout the interaction. When treating large degrees of freedom at the macroscopic level,
3063:
1346:
extends the notion of rate of change of an object's momentum to include the effects of an object "losing mass". (These generalizations/extensions are derived from Newton's laws, say, by decomposing a solid body into a collection of points.)
4684:
5420:
has no longer been an independent theory. Instead, classical mechanics is now considered an approximate theory to the more general quantum mechanics. Emphasis has shifted to understanding the fundamental forces of nature as in the
3400:
1878:
4885:
5250:. Here they are distinguished from earlier attempts at explaining similar phenomena, which were either incomplete, incorrect, or given little accurate mathematical expression. Newton also enunciated the principles of
1054:
shows that the long term predictions of classical mechanics are not reliable. Classical mechanics provides accurate results when studying objects that are not extremely massive and have speeds not approaching the
3803:
1889:. However, from the perspective of the faster car, the slower car is moving 10 km/h to the west, often denoted as −10 km/h where the sign implies opposite direction. Velocities are directly additive as
3785:
2745:
as a definition of force and mass, while others consider it a fundamental postulate, a law of nature. Either interpretation has the same mathematical consequences, historically known as "Newton's Second Law":
3138:
4567:
becomes useful. Statistical mechanics describes the behavior of large (but countable) numbers of particles and their interactions as a whole at the macroscopic level. Statistical mechanics is mainly used in
3572:
2978:
2047:
1994:
1389:
Classical mechanics assumes that matter and energy have definite, knowable attributes such as location in space and speed. Non-relativistic mechanics also assumes that forces act instantaneously (see also
4069:
3307:
2190:
3522:
242:
2107:
4912:
circling in a magnetic field. The (rest) mass of an electron is 511 keV. So the frequency correction is 1% for a magnetic vacuum tube with a 5.11 kV direct current accelerating voltage.
2752:
4766:
2467:
3901:
2697:
For some problems, it is convenient to use rotating coordinates (reference frames). Thereby one can either keep a mapping to a convenient inertial frame, or introduce additionally a fictitious
3797:
is the total potential energy (which is defined as a work of involved forces to rearrange mutual positions of bodies), obtained by summing the potential energies corresponding to each force
3154:
to zero as time progresses. In this case, an equivalent viewpoint is that the kinetic energy of the particle is absorbed by friction (which converts it to heat energy in accordance with the
7203:
2911:
5645:
5179:
was proposing abstract mathematical laws for the motion of objects. He may (or may not) have performed the famous experiment of dropping two cannonballs of different weights from the
5183:, showing that they both hit the ground at the same time. The reality of that particular experiment is disputed, but he did carry out quantitative experiments by rolling balls on an
4958:
1094:
is the branch of classical mechanics that is concerned with the analysis of force and torque acting on a physical system that does not experience an acceleration, but rather is in
5899:
2727:, such as an electro-static field (caused by static electrical charges), electro-magnetic field (caused by moving charges), or gravitational field (caused by mass), among others.
1196:
on the generalized coordinates, velocities and momenta; therefore, both contain the same information for describing the dynamics of a system. There are other formulations such as
4364:. Both theories provide interpretations of classical mechanics and describe the same physical phenomena. Hamiltonian mechanics has a close relationship with geometry (notably,
1890:
5470:
266:
6618:
4358:
2154:
2993:
1043:). These advances, made predominantly in the 18th and 19th centuries, extended beyond earlier works; they are, with some modification, used in all areas of modern physics.
177:
Diagram of orbital motion of a satellite around the Earth, showing perpendicular velocity and acceleration (force) vectors, represented through a classical interpretation
5358:
Some difficulties were discovered in the late 19th century that could only be resolved by more modern physics. Some of these difficulties related to compatibility with
2287:
Acceleration represents the velocity's change over time. Velocity can change in magnitude, direction, or both. Occasionally, a decrease in the magnitude of velocity "
1126:
goes beyond merely describing objects' behavior and also considers the forces which explain it. Some authors (for example, Taylor (2005) and
Greenwood (1997)) include
5244:; and hence laid the foundations for classical mechanics. Both Newton's second and third laws were given the proper scientific and mathematical treatment in Newton's
2928:
As an example, assume that friction is the only force acting on the particle, and that it may be modeled as a function of the velocity of the particle, for example:
2462:
4379:
In this formalism, the dynamics of a system are governed by
Hamilton's equations, which express the time derivatives of position and momentum variables in terms of
2356:
4213:
6447:
4135:
1139:
While the term "Newtonian mechanics" is sometimes used as a synonym for non-relativistic classical physics, it can also refer to a particular formalism based on
4253:
6553:
4614:
4285:
4233:
4178:
4158:
5110:, as we know it. These later became decisive factors in forming modern science, and their early application came to be known as classical mechanics. In his
3339:
4299:) throughout the time evolution of the system. This constraint allows the calculation of the equations of motion of the system using Lagrange's equations.
6311:
2365:
appears that there are other forces that enter the equations of motion solely as a result of the relative acceleration. These forces are referred to as
7183:
2859:. The net force on a particle is thus equal to the rate of change of the momentum of the particle with time. Since the definition of acceleration is
1830:
4805:
5429:. Classical mechanics is a theory useful for the study of the motion of non-quantum mechanical, low-energy particles in weak gravitational fields.
1116:
that cause them to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of
5054:. These have more momentum and therefore shorter De Broglie wavelengths than massless particles, such as light, with the same kinetic energies.
7475:
3527:
For extended objects composed of many particles, the kinetic energy of the composite body is the sum of the kinetic energies of the particles.
6521:
5246:
3885:{\displaystyle \mathbf {F} \cdot \Delta \mathbf {r} =-\mathbf {\nabla } E_{\mathrm {p} }\cdot \Delta \mathbf {r} =-\Delta E_{\mathrm {p} }\,.}
7245:
932:
5187:. His theory of accelerated motion was derived from the results of such experiments and forms a cornerstone of classical mechanics. In 1673
7564:
3741:
3710:{\displaystyle W=\Delta E_{\mathrm {k} }=E_{\mathrm {k_{2}} }-E_{\mathrm {k_{1}} }={\tfrac {1}{2}}m\left(v_{2}^{\,2}-v_{1}^{\,2}\right).}
521:
6610:
6216:
3078:
2723:
A force in physics is any action that causes an object's velocity to change; that is, to accelerate. A force originates from within a
1367:
640:
2987:
is a positive constant, the negative sign states that the force is opposite the sense of the velocity. Then the equation of motion is
5465:
2934:
6733:
5460:
5263:
2277:{\displaystyle \mathbf {a} ={\mathrm {d} \mathbf {v} \over \mathrm {d} t}={\mathrm {d^{2}} \mathbf {r} \over \mathrm {d} t^{2}}.}
613:
4540:
Many branches of classical mechanics are simplifications or approximations of more accurate forms; two of the most accurate being
1289:, which provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk
1208:. All equations of motion for particles and fields, in any formalism, can be derived from the widely applicable result called the
141:
7158:
7135:
6891:
6839:
4017:
3269:
2005:
1952:
1946:
in the directions of motion of each object respectively, then the velocity of the first object as seen by the second object is:
113:
7443:
6743:
6481:
5397:. As experiments reached the atomic level, classical mechanics failed to explain, even approximately, such basic things as the
4589:
3466:
198:
2834:{\displaystyle \mathbf {F} ={\mathrm {d} \mathbf {p} \over \mathrm {d} t}={\mathrm {d} (m\mathbf {v} ) \over \mathrm {d} t}.}
6359:
6340:
6321:
6293:
6272:
6251:
6230:
6198:
6174:
6155:
6112:
6057:
5945:
5877:
5796:
5768:
5739:
5710:
5604:
4559:
When both quantum mechanics and classical mechanics cannot apply, such as at the quantum level with many degrees of freedom,
1193:
989:
6026:
On a general method of expressing the paths of light, & of the planets, by the coefficients of a characteristic function
6770:
6188:
3993:{\displaystyle -\Delta E_{\mathrm {p} }=\Delta E_{\mathrm {k} }\Rightarrow \Delta (E_{\mathrm {k} }+E_{\mathrm {p} })=0\,.}
120:
94:
63:
5075:
The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in
4734:
3225:, while the weak form does not. Illustrations of the weak form of Newton's third law are often found for magnetic forces.
1366:.) Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the additional
6869:
6580:
595:
5895:
2058:
6782:
6102:
6760:
7238:
6572:
6082:
6007:
5850:
5823:
5681:
5654:
5571:
1784:
that is observed to elapse between any given pair of events is the same for all observers. In addition to relying on
925:
160:
127:
17:
4095:(also known as the principle of least action). It was introduced by the Italian-French mathematician and astronomer
7168:
6993:
4784:
is an approximation of the relativistic equation for bodies moving with low speeds compared to the speed of light.
2879:
2325:
in which the mechanical laws of nature take a comparatively simple form. These special reference frames are called
1378:
while it is moving. However, the results for point particles can be used to study such objects by treating them as
5440:
5258:. In mechanics, Newton was also the first to provide the first correct scientific and mathematical formulation of
887:
7188:
7090:
6988:
6809:
6145:
5363:
5069:
261:
4990:
in 1927, accelerated by 54 V, had a wavelength of 0.167 nm, which was long enough to exhibit a single
109:
42:
7391:
5138:
5063:
2918:
2698:
1205:
516:
256:
98:
4524:
of the
Lagrangian, and in many situations of physical interest it is equal to the total energy of the system.
2295:, but generally any change in the velocity over time, including deceleration, is referred to as acceleration.
1330:
applied to it. Classical mechanics also describes the more complex motions of extended non-pointlike objects.
7073:
6262:
4930:
4138:
2318:
1181:
4924:
is not much smaller than other dimensions of the system. For non-relativistic particles, this wavelength is
4572:
for systems that lie outside the bounds of the assumptions of classical thermodynamics. In the case of high
2440:, then the relation between the space-time coordinates of the same event observed from the reference frames
7585:
7231:
6983:
6420:
5367:
5043:
2361:
1318:, that is, objects with negligible size. The motion of a point particle is determined by a small number of
918:
905:
666:
589:
511:
354:
5813:
5624:
7528:
7178:
7037:
6834:
5961:
Fraser, Craig (1983). "J. L. Lagrange's Early
Contributions to the Principles and Methods of Mechanics".
5306:
4092:
2304:
1046:
If the present state of an object that obeys the laws of classical mechanics is known, it is possible to
585:
386:
6928:
5020:
More practical examples of the failure of classical mechanics on an engineering scale are conduction by
1900:
Mathematically, if the velocity of the first object in the previous discussion is denoted by the vector
364:
7359:
7332:
6978:
6973:
6896:
6799:
6765:
6728:
6587:
6474:
5480:
5233:
5225:
5198:
4321:
4264:
2718:
2689:
is not a constant in classical mechanics, nor does the special position given to the speed of light in
1197:
1140:
805:
694:
620:
480:
413:
5289:, worked on the assumption that classical mechanics would be able to explain all phenomena, including
4600:
unifying GR and QFT in the sense that it could be used when objects become extremely small and heavy.
3158:), and the particle is slowing down. This expression can be further integrated to obtain the position
3058:{\displaystyle -\lambda \mathbf {v} =m\mathbf {a} =m{\mathrm {d} \mathbf {v} \over \mathrm {d} t}\,.}
6943:
6859:
6513:
1209:
1004:
559:
38:
6390:
4327:
4074:
is constant in time. It is often useful, because many commonly encountered forces are conservative.
7465:
6814:
6755:
6738:
6723:
6668:
5251:
5193:
835:
679:
6792:
6545:
3531:
2597:
2308:
785:
549:
134:
87:
5786:
5319:'s contribution was realising Newton's ideas in the language of modern mathematics, now called
5087:. The development of classical mechanics lead to the development of many areas of mathematics.
4101:
4099:
in his presentation to the Turin
Academy of Science in 1760 culminating in his 1788 grand opus,
825:
7549:
7411:
7163:
7153:
6918:
6881:
6854:
6748:
6222:
5359:
5343:
5333:
3155:
2742:
2690:
2582:{\displaystyle {\begin{aligned}x'&=x-tu,\\y'&=y,\\z'&=z,\\t'&=t.\end{aligned}}}
2118:
1272:
1173:
1095:
1072:
1028:
830:
647:
5997:
5937:
5756:
5698:
3181:
can sometimes be used to deduce the forces acting on a particle: if it is known that particle
7554:
7523:
7386:
7307:
7210:
7117:
7003:
6998:
6787:
6700:
6675:
6467:
5884:
5727:
5406:
5382:
5351:
5329:
5316:
5180:
4921:
4564:
4545:
4313:
4308:
4096:
3178:
1286:
1185:
1040:
1024:
981:
840:
815:
501:
319:
5929:
5840:
7513:
7337:
7297:
7124:
6844:
6601:
5495:
5426:
5347:
5320:
5099:
4581:
4560:
4317:
4088:
4083:
2593:
1482:
1391:
1213:
1177:
1151:
1121:
1036:
1032:
999:. It consists of the physical concepts based on the 17th century foundational works of Sir
961:
860:
820:
728:
724:
716:
706:
496:
489:
245:
4897:
is the classical frequency of an electron (or other charged particle) with kinetic energy
2332:
855:
8:
7488:
7347:
7342:
7302:
7279:
7255:
6933:
6913:
6819:
6680:
6450:
Free videos of actual course lectures with links to lecture notes, assignments and exams.
5903:
5241:
5210:
4679:{\displaystyle \mathbf {p} ={\frac {m\mathbf {v} }{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}\,,}
4585:
4365:
4292:
4288:
3312:
More generally, if the force varies as a function of position as the particle moves from
2321:
in any state of motion, classical mechanics assumes the existence of a special family of
1777:
1646:
1250:
1236:
1169:
1075:
in classical physics, as representing the field in its most developed and accurate form.
996:
949:
635:
576:
554:
299:
294:
289:
6414:
4183:
2383:. For observers in each of the reference frames an event has space-time coordinates of (
2052:
When both objects are moving in the same direction, this equation can be simplified to:
7544:
7421:
7416:
7369:
7148:
6864:
6777:
6505:
6437:
6303:
6212:
5978:
5485:
5475:
5286:
5281:
was formulated entirely in terms of long-established geometric methods in emulation of
5206:
5188:
5172:
5115:
5091:
5036:
5014:
5006:
4593:
4577:
4541:
4521:
4380:
4238:
4108:
3420:
2852:
2609:
2322:
1789:
1737:
1280:
1276:
1221:
1201:
1127:
1068:
1064:
765:
506:
381:
349:
309:
4263:
energy of the system, respectively. The stationary action principle requires that the
3395:{\displaystyle W=\int _{C}\mathbf {F} (\mathbf {r} )\cdot \mathrm {d} \mathbf {r} \,.}
7559:
7508:
7453:
7433:
7319:
7107:
7079:
6961:
6938:
6886:
6804:
6690:
6426:
6383:
6355:
6336:
6317:
6289:
6283:
6268:
6247:
6241:
6226:
6194:
6184:
6170:
6151:
6108:
6078:
6053:
6030:
6003:
5941:
5930:
5873:
5846:
5819:
5792:
5764:
5735:
5706:
5677:
5650:
5600:
5577:
5567:
5490:
5410:
5302:
5298:
5216:
5134:
5032:
5021:
4373:
4369:
3151:
1718:
1656:
1528:
1363:
1307:
1172:
are derived from the scalar quantity by some underlying principle about the scalar's
1060:
775:
732:
689:
684:
625:
401:
391:
284:
3895:
The decrease in the potential energy is equal to the increase in the kinetic energy
2605:
1350:
In reality, the kind of objects that classical mechanics can describe always have a
7498:
7438:
7364:
7067:
7043:
7019:
6849:
6595:
5970:
5626:
Elements of
Mechanics Including Kinematics, Kinetics and Statics: with applications
5564:
Experimental
Philosophy and the Birth of Empirical Science: Boyle, Locke and Newton
5455:
5294:
5267:
5255:
5047:
4983:
4549:
4270:
4260:
4218:
4163:
4143:
3725:
3242:
3174:
2373:
2366:
1698:
1548:
1462:
1416:
1335:
1217:
1165:
1156:
1144:
1105:
870:
850:
795:
790:
736:
711:
566:
424:
369:
344:
1059:. With objects about the size of an atom's diameter, it becomes necessary to use
7518:
7428:
7374:
7274:
7055:
6824:
6718:
6141:
5867:
5671:
5640:
5390:
5176:
5154:
4968:
4597:
3428:
2724:
2326:
1894:
1677:
1622:
1612:
1588:
1510:
1420:
1371:
1343:
1331:
1180:, which uses generalized coordinates and corresponding generalized velocities in
1109:
865:
810:
760:
755:
674:
6441:
5373:
A second set of difficulties were related to thermodynamics. When combined with
7448:
7403:
7381:
7269:
7098:
6923:
6906:
6876:
6663:
6397:
6183:
5446:
5422:
5374:
5237:
5184:
5002:
4902:
4569:
4553:
4256:
3557:
3443:
3432:
3260:
3238:
3234:
3069:
2702:
2686:
2621:
2112:
Or, by ignoring direction, the difference can be given in terms of speed only:
1873:{\displaystyle \mathbf {v} ={\mathrm {d} \mathbf {r} \over \mathrm {d} t}\,\!}
1714:
1688:
1602:
1492:
1383:
1315:
1290:
1283:
theories of relativity), for bodies whose speed is close to the speed of light.
1161:
1056:
1008:
892:
800:
701:
418:
6432:
6379:(an introductory text, uses algebra with optional sections involving calculus)
5845:(4th ed.). New York: Dover Publications Inc. Introduction, pp. xxi–xxix.
5201:. The work is also the first modern treatise in which a physical problem (the
4880:{\displaystyle f=f_{\mathrm {c} }{\frac {m_{0}}{m_{0}+{\frac {T}{c^{2}}}}}\,,}
1379:
7579:
7458:
7143:
7025:
6967:
5398:
5378:
4987:
4982:
before it happens with heavier particles. For example, the electrons used by
3331:
3170:
1785:
1781:
1112:(objects), and systems of bodies (groups of objects) without considering the
1012:
780:
607:
7223:
6034:
5581:
2672:(the acceleration of a particle is the same in any inertial reference frame)
2423:. Assuming time is measured the same in all reference frames, if we require
1752:. In general, the point particle does not need to be stationary relative to
1382:
objects, made of a large number of collectively acting point particles. The
7483:
7031:
6901:
6710:
6685:
6648:
6490:
6098:
5872:(illustrated ed.). Springer Science & Business Media. p. 30.
5221:
5202:
5050:. It is more often accurate because it describes particles and bodies with
5025:
4576:
objects approaching the speed of light, classical mechanics is enhanced by
4296:
2730:
2172:
2165:
1472:
1051:
1000:
845:
770:
459:
339:
2873:, the second law can be written in the simplified and more familiar form:
7049:
6658:
6537:
6419:
Sussman, Gerald Jay & Wisdom, Jack & Mayer, Meinhard E. (2001).
6307:
5918:
Goldstein, Herbert (1950). Classical
Mechanics (1st ed.). Addison-Wesley.
5312:
5209:
then analyzed mathematically and constitutes one of the seminal works of
5160:
5080:
5010:
4991:
1943:
1636:
1189:
1117:
1088:
Classical mechanics was traditionally divided into three main branches.
1047:
6406:
6002:(2nd ed.). Cambridge University Press. pp. 18–20, 23, 46, 51.
5982:
5339:
5285:. Newton, and most of his contemporaries, with the notable exception of
4532:
995:
The earliest formulation of classical mechanics is often referred to as
7503:
7493:
7173:
7061:
6208:
5974:
5224:(1643–1727), an influential figure in the history of physics and whose
5107:
5084:
5029:
3150:
is the initial velocity. This means that the velocity of this particle
2181:
2177:
1999:
Similarly, the first object sees the velocity of the second object as:
1821:
1632:
1403:
1351:
1314:
For simplicity, classical mechanics often models real-world objects as
1100:
965:
957:
630:
304:
6454:
6436:
Movies and photos of hundreds of working mechanical-systems models at
5232:
Newton founded his principles of natural philosophy on three proposed
988:
distinguishes this type of mechanics from physics developed after the
7354:
5095:
5051:
4994:
4979:
4796:
4788:
2682:(the force on a particle is the same in any inertial reference frame)
1319:
1302:
652:
6349:
6104:
Unrolling Time: Christiaan
Huygens and the Mathematization of Nature
6024:
5129:
1160:
properties of motion representing the system as a whole—usually its
76:
6695:
6636:
6459:
6376:
5818:(Reprint of 1977 ed.). Courier Dover Publications. p. 1.
5646:
A Treatise on the
Analytical Dynamics of Particles and Rigid Bodies
5409:. The effort at resolving these problems led to the development of
5274:
5240:, his second law of acceleration (mentioned above), and the law of
4792:
4573:
3780:{\displaystyle \mathbf {F} =-\mathbf {\nabla } E_{\mathrm {p} }\,.}
3721:
3436:
2856:
2738:
2314:
1817:
1812:
1801:
1730:
1598:
1538:
1452:
1375:
1359:
1339:
977:
571:
454:
429:
4920:
The ray approximation of classical mechanics breaks down when the
4596:(GR) becomes applicable. However, until now there is no theory of
4584:
is not negligibly small for a given application), deviations from
3419:
is the same no matter what path is taken, the force is said to be
1334:
provide extensions to Newton's laws in this area. The concepts of
6653:
6641:
6529:
6429:(Cambridge lecture notes on Lagrangian and Hamiltonian formalism)
6164:
5521:
is the difference of the particle's initial and final positions:
5417:
5394:
5386:
5259:
5168:
5149:
5119:
5076:
4998:
3424:
3166:
3133:{\displaystyle \mathbf {v} =\mathbf {v} _{0}e^{{-\lambda t}/{m}}}
2733:
was the first to mathematically express the relationship between
1666:
1090:
969:
544:
397:
314:
173:
6285:
Introduction to Classical Mechanics: With Problems and Solutions
6072:
4603:
1232:
Alternatively, a division can be made by region of application:
7207:
5282:
5145:
5123:
5103:
4915:
4105:. Lagrangian mechanics describes a mechanical system as a pair
4008:
2973:{\displaystyle \mathbf {F} _{\rm {R}}=-\lambda \mathbf {v} \,,}
1578:
1568:
1426:
1262:
1244:
1020:
953:
603:
449:
359:
5471:
List of textbooks on classical mechanics and quantum mechanics
4608:
In special relativity, the momentum of a particle is given by
1729:. A simple coordinate system might describe the position of a
6302:
5402:
5290:
3790:
If all the forces acting on a particle are conservative, and
3427:
is a conservative force, as is the force due to an idealized
2734:
2714:
1805:
1722:
1558:
1442:
1327:
1258:
1254:
1113:
1016:
439:
434:
376:
5332:. Lagrangian mechanics was in turn re-formulated in 1833 by
1067:
is needed. In cases where objects become extremely massive,
992:, all of which revealed limitations in classical mechanics.
5164:
4580:. In case that objects become extremely heavy (i.e., their
4064:{\displaystyle \sum E=E_{\mathrm {k} }+E_{\mathrm {p} }\,,}
1773:
1323:
1240:
973:
444:
407:
6260:
6239:
5416:
Since the end of the 20th century, classical mechanics in
5013:
and see quantum diffraction from the periodic patterns of
4324:, Hamiltonian mechanics replaces (generalized) velocities
3302:{\displaystyle W=\mathbf {F} \cdot \Delta \mathbf {r} \,.}
2042:{\displaystyle \mathbf {v'} =\mathbf {v} -\mathbf {u} \,.}
1989:{\displaystyle \mathbf {u} '=\mathbf {u} -\mathbf {v} \,.}
1297:
1143:. Newtonian mechanics in this sense emphasizes force as a
4180:
within that space called a Lagrangian. For many systems,
3517:{\displaystyle E_{\mathrm {k} }={\tfrac {1}{2}}mv^{2}\,.}
1266:
1063:. To describe velocities approaching the speed of light,
237:{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}
5761:
Mechanical Systems, Classical Models: Particle Mechanics
5370:, often still considered a part of classical mechanics.
6330:
6288:(1st ed.). Cambridge: Cambridge University Press.
6022:
5639:
4787:
For example, the relativistic cyclotron frequency of a
4091:
is a formulation of classical mechanics founded on the
1410:
6444:
of classic texts on mechanical design and engineering.
4273:
4221:
4186:
4166:
4146:
4111:
3645:
3486:
3209:. The strong form of Newton's third law requires that
1188:, which uses coordinates and corresponding momenta in
6352:
Classical Dynamics of Particles and Systems (5th ed.)
5622:
4933:
4808:
4737:
4617:
4389:
4330:
4241:
4020:
3904:
3806:
3744:
3575:
3469:
3342:
3272:
3081:
2996:
2937:
2882:
2755:
2627:
The transformations have the following consequences:
2465:
2335:
2193:
2121:
2061:
2008:
1955:
1833:
1386:
of a composite object behaves like a point particle.
201:
6433:
Kinematic Models for Design Digital Library (KMODDL)
5436:
5001:
with atomic spacing of 0.215 nm. With a larger
4761:{\displaystyle \mathbf {p} \approx m\mathbf {v} \,.}
3251:
is applied to a particle that makes a displacement Δ
1913:
and the velocity of the second object by the vector
1176:. Two dominant branches of analytical mechanics are
6421:
Structure and Interpretation of Classical Mechanics
6313:
Structure and Interpretation of Classical Mechanics
5696:
5669:
4588:become apparent and can be quantified by using the
2313:While the position, velocity and acceleration of a
101:. Unsourced material may be challenged and removed.
6131:
6052:. Cambridge New York: Cambridge university press.
5936:(5. ed.). Belmont, CA: Brooks/Cole. pp.
5811:
5784:
4952:
4879:
4760:
4678:
4512:
4352:
4279:
4247:
4227:
4207:
4172:
4152:
4129:
4063:
3992:
3884:
3779:
3709:
3516:
3394:
3301:
3132:
3057:
2972:
2905:
2833:
2581:
2350:
2276:
2148:
2102:{\displaystyle \mathbf {u} '=(u-v)\mathbf {d} \,.}
2101:
2041:
1988:
1872:
1721:centered on an arbitrary fixed reference point in
980:. The development of classical mechanics involved
236:
7184:Statal Institute of Higher Education Isaac Newton
6264:Course of Theoretical Physics, Vol. 1 – Mechanics
4556:, and does not have a superior "classical" form.
1869:
7577:
6140:
5754:
5725:
5005:, it would seem relatively easy to increase the
4360:used in Lagrangian mechanics with (generalized)
3330:, the work done on the particle is given by the
1071:becomes applicable. Some modern sources include
990:revolutions in physics of the early 20th century
982:substantial change in the methods and philosophy
6350:Thornton, Stephen T.; Marion, Jerry B. (2003).
6207:
5928:Thornton, Stephen T.; Marion, Jerry B. (2004).
3542:done on the particle as it moves from position
1253:, for materials modelled as a continuum, e.g.,
6391:Preferred Frames of Reference & Relativity
5927:
5425:and its more modern extensions into a unified
5393:was not explained without the introduction of
5366:. The resolution of these problems led to the
2612:. The limiting case applies when the velocity
7253:
7239:
6475:
5865:
5705:(12th ed.). Prentice Hall. p. 298.
4604:Newtonian approximation to special relativity
4372:) and serves as a link between classical and
3405:If the work done in moving the particle from
2906:{\displaystyle \mathbf {F} =m\mathbf {a} \,.}
1820:of displacement with time, is defined as the
1780:), time is considered an absolute, i.e., the
1342:used to describe one-dimensional motion. The
926:
6448:MIT OpenCourseWare 8.01: Classical Mechanics
6165:Feynman, Richard; Phillips, Richard (1998).
6047:
5914:
5912:
5734:(2nd ed.). Cambridge University Press.
4916:Classical approximation to quantum mechanics
3720:Conservative forces can be expressed as the
3534:states that for a particle of constant mass
5932:Classical dynamics of particles and systems
5597:Science in the Twentieth Century and Beyond
5466:List of publications in classical mechanics
5247:Philosophiæ Naturalis Principia Mathematica
1227:
1003:, and the mathematical methods invented by
23:
7246:
7232:
6482:
6468:
6187:; Charles P. Poole; John L. Safko (2002).
6077:. Cambridge University Press. p. 75.
6048:Doran, Chris; Lasenby, Anthony N. (2003).
5159:published in 1609. He concluded, based on
4997:when reflecting from the face of a nickel
4536:Domain of validity for classical mechanics
2693:have a counterpart in classical mechanics.
2448:, which are moving at a relative velocity
2180:of the velocity with respect to time (the
1031:and others, leading to the development of
933:
919:
24:
6107:. Cambridge: Cambridge University Press.
6073:Rob Iliffe & George E. Smith (2016).
5995:
5909:
5805:
5649:. Cambridge University Press. Chapter 1.
5561:
4873:
4754:
4672:
4057:
3986:
3878:
3773:
3693:
3674:
3510:
3388:
3295:
3051:
2966:
2899:
2142:
2095:
2035:
1982:
1868:
161:Learn how and when to remove this message
5896:MIT physics 8.01 lecture notes (page 12)
5633:
5618:
5616:
5461:List of equations in classical mechanics
5338:
5311:
5215:
5175:was happening around the same time that
5128:
5042:Classical mechanics is the same extreme
4531:
4302:
2646:′ of a particle from the perspective of
2604:). This group is a limiting case of the
2176:, or rate of change of velocity, is the
1301:
1192:. Both formulations are equivalent by a
1048:determine how it will move in the future
172:
32:This is an accepted version of this page
5866:Knudsen, Jens M.; Hjorth, Poul (2012).
5842:The variational principles of mechanics
5838:
5832:
5699:"Kinematics and kinetics of a particle"
5112:Elementa super demonstrationem ponderum
4953:{\displaystyle \lambda ={\frac {h}{p}}}
4500:
4458:
4438:
4399:
4077:
3263:of the force and displacement vectors:
3162:of the particle as a function of time.
2184:of the position with respect to time):
1934:is the speed of the second object, and
1776:. In pre-Einstein relativity (known as
1298:Description of objects and their motion
1083:
14:
7578:
7444:Atomic, molecular, and optical physics
5960:
5297:. Even when discovering the so-called
5118:introduced the concept of "positional
4590:parameterized post-Newtonian formalism
4383:of a function called the Hamiltonian:
4316:emerged in 1833 as a reformulation of
2708:
2298:
1824:of the position with respect to time:
7227:
6734:Newton's law of universal gravitation
6463:
6281:
6261:Landau, L.D.; Lifshitz, E.M. (1972).
6240:Kleppner, D.; Kolenkow, R.J. (1973).
6097:
5963:Archive for History of Exact Sciences
5778:
5613:
5264:Newton's law of universal gravitation
5228:form the basis of classical mechanics
4527:
4287:must remain at a stationary point (a
2317:can be described with respect to any
1795:
1011:and others to describe the motion of
615:Newton's law of universal gravitation
59:Description of large objects' physics
6892:Newton's theorem of revolving orbits
6489:
5663:
5594:
2369:, inertia forces, or pseudo-forces.
1133:
1050:, and how it has moved in the past.
99:adding citations to reliable sources
70:
64:Classical Mechanics (disambiguation)
6840:Leibniz–Newton calculus controversy
6581:standing on the shoulders of giants
5676:. Taylor & Francis. p. 1.
5377:, classical mechanics leads to the
5273:Newton had previously invented the
3724:of a scalar function, known as the
596:Mechanics of planar particle motion
204:
56:
6125:
6091:
5996:Hand, L. N.; Finch, J. D. (1998).
5305:phenomenon) he maintained his own
4821:
4496:
4489:
4484:
4465:
4453:
4434:
4427:
4422:
4406:
4394:
4051:
4036:
3971:
3956:
3944:
3935:
3926:
3917:
3908:
3872:
3863:
3849:
3840:
3830:
3815:
3767:
3757:
3629:
3607:
3591:
3582:
3476:
3379:
3287:
3228:
3041:
3029:
2946:
2818:
2797:
2780:
2768:
2254:
2236:
2218:
2206:
1930:is the speed of the first object,
1858:
1846:
1362:, is more accurately described by
57:
7597:
6369:
6333:Essential Dynamics and Relativity
6075:The Cambridge Companion to Newton
3197:must exert an equal and opposite
1310:is a part of classical mechanics.
7169:Isaac Newton Group of Telescopes
6398:Classical Mechanics Course Notes
6193:(3rd ed.). Addison Wesley.
6050:Geometric algebra for physicists
6023:Hamilton, William Rowan (1833).
5629:. E. and F. N. Spon. p. 85.
5439:
5389:is not a well-defined quantity.
5207:idealized by a set of parameters
5167:, that the planet's orbits were
5163:'s observations on the orbit of
4750:
4739:
4633:
4619:
3853:
3819:
3808:
3746:
3384:
3368:
3360:
3291:
3280:
3092:
3083:
3034:
3015:
3004:
2962:
2940:
2895:
2884:
2808:
2773:
2757:
2247:
2211:
2195:
2091:
2064:
2031:
2023:
2011:
1978:
1970:
1958:
1893:; they must be dealt with using
1851:
1835:
900:
899:
886:
219:
75:
7565:Timeline of physics discoveries
7189:Newton International Fellowship
6870:generalized Gauss–Newton method
6783:Newton's method in optimization
6147:The Feynman Lectures on Physics
6066:
6041:
6016:
5989:
5954:
5921:
5889:
5869:Elements of Newtonian Mechanics
5859:
5703:Engineering Mechanics: Dynamics
5508:
5070:Timeline of classical mechanics
5068:For a chronological guide, see
4448:
3259:by the force is defined as the
2592:This set of formulas defines a
2159:
86:needs additional citations for
6134:Fundamental University Physics
5748:
5719:
5690:
5623:Thomas Wallace Wright (1896).
5588:
5555:
5148:explanation of the motions of
5064:History of classical mechanics
4728:is approximately zero, and so
4353:{\displaystyle {\dot {q}}^{i}}
4124:
4112:
3977:
3947:
3941:
3372:
3364:
3217:act along the line connecting
2919:ordinary differential equation
2812:
2801:
2087:
2075:
1788:, classical mechanics assumes
13:
1:
6218:Classical Mechanics (5th ed.)
6132:Alonso, M.; Finn, J. (1992).
5732:Dynamics of Multibody Systems
5548:
4693:is the particle's rest mass,
3165:Important forces include the
2743:Newton's second law of motion
2362:Non-inertial reference frames
1397:
1358:small particles, such as the
1216:, a statement which connects
522:Koopman–von Neumann mechanics
6810:Newton's theorem about ovals
6410:". Physics Education. 1999.
6331:O'Donnell, Peter J. (2015).
6243:An Introduction to Mechanics
5791:. University Science Books.
5697:Russell C. Hibbeler (2009).
5670:Joseph Stiles Beggs (1983).
5368:special theory of relativity
5346:developed an alternative to
5044:high frequency approximation
4771:Thus the Newtonian equation
2741:. Some physicists interpret
1792:for the structure of space.
1768:is defined as a function of
1744:that points from the origin
1740:notated by an arrow labeled
1717:is defined in relation to a
590:Non-inertial reference frame
7:
7529:Quantum information science
7179:Sir Isaac Newton Sixth Form
6835:Corpuscular theory of light
6761:Schrödinger–Newton equation
5839:Lanczos, Cornelius (1970).
5812:Donald T Greenwood (1997).
5785:John Robert Taylor (2005).
5599:, Cambridge: Polity Press,
5562:Ben-Chaim, Michael (2004),
5432:
5364:Michelson–Morley experiment
5307:corpuscular theory of light
5122:" and the use of component
4552:is an approximation to the
4267:of the system derived from
4093:stationary-action principle
2305:Inertial frame of reference
1206:Appell's equation of motion
1130:within classical dynamics.
1078:
517:Appell's equation of motion
387:Inertial frame of reference
10:
7602:
7360:Classical electromagnetism
6588:Notes on the Jewish Temple
5270:of motion of the planets.
5067:
5061:
5057:
5009:from around a radian to a
4716:is very small compared to
4322:Sir William Rowan Hamilton
4306:
4081:
4007:and states that the total
3556:is equal to the change in
3232:
2712:
2616:is very small compared to
2302:
2163:
1799:
1401:
1247:and other celestial bodies
1019:. Later, methods based on
984:of physics. The qualifier
61:
7537:
7474:
7402:
7318:
7290:
7262:
7197:
7134:
7089:
7012:
6954:
6709:
6629:
6564:
6497:
6413:Shapiro, Joel A. (2003).
6267:. Franklin Book Company.
6029:. Printed by P.D. Hardy.
5763:. Springer. p. 287.
5755:P. P. Teodorescu (2007).
5726:Ahmed A. Shabana (2003).
5114:, medieval mathematician
5094:of antiquity, among them
4978:Again, this happens with
2149:{\displaystyle u'=u-v\,.}
1210:principle of least action
1023:were developed by Euler,
1005:Gottfried Wilhelm Leibniz
7466:Condensed matter physics
6739:post-Newtonian expansion
6619:Corruptions of Scripture
6611:Ancient Kingdoms Amended
5502:
5252:conservation of momentum
5194:Horologium Oscillatorium
4003:This result is known as
2658:from the perspective of
1293:properties of materials.
1228:By region of application
680:Rotating reference frame
512:Hamilton–Jacobi equation
39:latest accepted revision
6929:Absolute space and time
6793:truncated Newton method
6766:Newton's laws of motion
6729:Newton's law of cooling
5641:Edmund Taylor Whittaker
5481:Newton's laws of motion
4709:is the speed of light.
4554:quantum theory of light
4520:The Hamiltonian is the
2719:Newton's laws of motion
2598:Galilean transformation
2309:Galilean transformation
1354:size. (The behavior of
1194:Legendre transformation
1141:Newton's laws of motion
1098:with its environment.
1015:under the influence of
621:Newton's laws of motion
481:Newton's laws of motion
7550:Nobel Prize in Physics
7412:Relativistic mechanics
7164:Isaac Newton Telescope
7154:Isaac Newton Institute
6924:Newton–Puiseux theorem
6919:Parallelogram of force
6907:kissing number problem
6897:Newton–Euler equations
6800:Gauss–Newton algorithm
6749:gravitational constant
6455:On Classical Mechanics
6453:Alejandro A. Torassa,
6389:Hoiland, Paul (2004).
6382:Fitzpatrick, Richard.
6223:Imperial College Press
6169:. Perseus Publishing.
6150:. Perseus Publishing.
5728:"Reference kinematics"
5566:, Aldershot: Ashgate,
5360:electromagnetic theory
5355:
5334:William Rowan Hamilton
5324:
5229:
5205:of a falling body) is
5152:was Johannes Kepler's
5141:
4954:
4881:
4762:
4680:
4537:
4514:
4354:
4281:
4249:
4229:
4209:
4174:
4160:and a smooth function
4154:
4131:
4065:
4005:conservation of energy
3994:
3886:
3781:
3711:
3518:
3452:of a particle of mass
3396:
3303:
3156:conservation of energy
3134:
3059:
2974:
2921:, which is called the
2907:
2835:
2691:relativistic mechanics
2583:
2352:
2278:
2150:
2103:
2043:
1990:
1874:
1760:is moving relative to
1311:
1273:Relativistic mechanics
1198:Hamilton–Jacobi theory
1073:relativistic mechanics
1029:William Rowan Hamilton
648:Simple harmonic motion
561:Euler's laws of motion
355:D'Alembert's principle
238:
178:
7555:Philosophy of physics
7118:Isaac Newton Gargoyle
7028: (nephew-in-law)
7004:Copernican Revolution
6999:Scientific Revolution
6860:Newton–Cotes formulas
6724:Newton's inequalities
6701:Structural coloration
6282:Morin, David (2008).
5407:photo-electric effect
5383:statistical mechanics
5352:Hamiltonian mechanics
5342:
5330:Joseph Louis Lagrange
5315:
5219:
5132:
4955:
4922:de Broglie wavelength
4882:
4763:
4681:
4565:statistical mechanics
4546:statistical mechanics
4535:
4515:
4355:
4314:Hamiltonian mechanics
4309:Hamiltonian mechanics
4303:Hamiltonian mechanics
4282:
4250:
4230:
4210:
4175:
4155:
4132:
4097:Joseph-Louis Lagrange
4066:
3995:
3887:
3782:
3712:
3519:
3439:is non-conservative.
3397:
3304:
3135:
3060:
2975:
2908:
2836:
2584:
2353:
2279:
2151:
2104:
2044:
1991:
1875:
1425:units with kg, m and
1305:
1287:Statistical mechanics
1186:Hamiltonian mechanics
1041:Hamiltonian mechanics
1025:Joseph-Louis Lagrange
502:Hamiltonian mechanics
320:Statistical mechanics
239:
176:
110:"Classical mechanics"
7514:Mathematical physics
7125:Astronomers Monument
6815:Newton–Pepys problem
6788:Apollonius's problem
6756:Newton–Cartan theory
6669:Newton–Okounkov body
6602:hypotheses non fingo
6591: (c. 1680)
5999:Analytical Mechanics
5496:Quantum field theory
5427:theory of everything
5391:Black-body radiation
5348:Lagrangian mechanics
5321:Lagrangian mechanics
5226:three laws of motion
5144:The first published
5100:Aristotelian physics
4931:
4806:
4735:
4615:
4582:Schwarzschild radius
4561:quantum field theory
4387:
4328:
4318:Lagrangian mechanics
4271:
4239:
4219:
4184:
4164:
4144:
4109:
4102:Mécanique analytique
4089:Lagrangian mechanics
4084:Lagrangian mechanics
4078:Lagrangian mechanics
4018:
3902:
3804:
3742:
3573:
3467:
3456:travelling at speed
3340:
3270:
3247:If a constant force
3189:on another particle
3152:decays exponentially
3079:
2994:
2935:
2880:
2753:
2594:group transformation
2463:
2351:{\displaystyle F=ma}
2333:
2291:" is referred to as
2191:
2119:
2059:
2006:
1953:
1831:
1483:angular acceleration
1413:derived "mechanical"
1392:Action at a distance
1275:(i.e. including the
1220:to their associated
1178:Lagrangian mechanics
1152:analytical mechanics
1084:Traditional division
1037:Lagrangian mechanics
1033:analytical mechanics
725:Angular acceleration
717:Rotational frequency
497:Lagrangian mechanics
490:Analytical mechanics
246:Second law of motion
199:
95:improve this article
62:For other uses, see
7586:Classical mechanics
7489:Atmospheric physics
7328:Classical mechanics
7256:branches of physics
6934:Luminiferous aether
6882:Newton's identities
6855:Newton's cannonball
6830:Classical mechanics
6820:Newtonian potential
6681:Newtonian telescope
6440:. Also includes an
6415:Classical Mechanics
6407:Classical Mechanics
6395:Horbatsch, Marko, "
6384:Classical Mechanics
6375:Crowell, Benjamin.
6213:Berkshire, Frank H.
6190:Classical Mechanics
5904:Library of Congress
5815:Classical Mechanics
5788:Classical Mechanics
5242:action and reaction
5211:applied mathematics
5037:integrated circuits
4586:Newtonian mechanics
4381:partial derivatives
4366:symplectic geometry
4208:{\textstyle L=T-V,}
4139:configuration space
3698:
3679:
3532:work–energy theorem
3435:. The force due to
3167:gravitational force
2709:Newtonian mechanics
2299:Frames of reference
1778:Galilean relativity
1647:kinematic viscosity
1429:
1251:Continuum mechanics
1237:Celestial mechanics
1182:configuration space
1170:equations of motion
997:Newtonian mechanics
956:of objects such as
946:Classical mechanics
577:Harmonic oscillator
555:Equations of motion
190:Classical mechanics
184:Part of a series on
29:Page version status
7545:History of physics
7159:Isaac Newton Medal
6964: (birthplace)
6778:Newtonian dynamics
6676:Newton's reflector
6438:Cornell University
6427:Classical Dynamics
6304:Gerald Jay Sussman
6185:Goldstein, Herbert
5975:10.1007/BF00328268
5906:Web Archives (PDF)
5902:2013-07-09 at the
5885:Extract of page 30
5595:Agar, Jon (2012),
5486:Special relativity
5476:Molecular dynamics
5356:
5325:
5230:
5203:accelerated motion
5189:Christiaan Huygens
5171:. This break with
5142:
5116:Jordanus de Nemore
5092:Greek philosophers
5015:integrated circuit
5007:angular resolution
4950:
4877:
4795:, or high voltage
4758:
4701:is the modulus of
4676:
4594:general relativity
4578:special relativity
4542:general relativity
4538:
4528:Limits of validity
4522:Legendre transform
4510:
4370:Poisson structures
4350:
4277:
4245:
4225:
4205:
4170:
4150:
4130:{\textstyle (M,L)}
4127:
4061:
3990:
3882:
3777:
3707:
3683:
3664:
3654:
3514:
3495:
3392:
3299:
3193:, it follows that
3179:Newton's third law
3130:
3055:
2970:
2923:equation of motion
2903:
2831:
2654:than its velocity
2610:special relativity
2602:Galilean transform
2579:
2577:
2348:
2274:
2146:
2099:
2039:
1986:
1870:
1796:Velocity and speed
1790:Euclidean geometry
1725:called the origin
1520:absorbed dose rate
1447:unitless (radian)
1408:
1368:degrees of freedom
1312:
1202:Routhian mechanics
1128:special relativity
1069:general relativity
1065:special relativity
893:Physics portal
507:Routhian mechanics
382:Frame of reference
234:
179:
35:
7573:
7572:
7560:Physics education
7509:Materials science
7476:Interdisciplinary
7434:Quantum mechanics
7221:
7220:
7113: (sculpture)
7080:Abraham de Moivre
7034: (professor)
6962:Woolsthorpe Manor
6914:Newton's quotient
6887:Newton polynomial
6845:Newton's notation
6576: (1661–1665)
6404:Rosu, Haret C., "
6361:978-0-534-40896-1
6342:978-1-4665-8839-4
6323:978-0-262-19455-6
6295:978-0-521-87622-3
6274:978-0-08-016739-8
6253:978-0-07-035048-9
6232:978-1-86094-424-6
6200:978-0-201-65702-9
6176:978-0-201-32841-7
6157:978-0-7382-0092-7
6136:. Addison-Wesley.
6114:978-0-521-34140-0
6059:978-0-521-48022-2
5947:978-0-534-40896-1
5879:978-3-642-97599-8
5798:978-1-891389-22-1
5770:978-1-4020-5441-9
5741:978-0-521-54411-5
5712:978-0-13-607791-6
5606:978-0-7456-3469-2
5514:The displacement
5491:Quantum mechanics
5411:quantum mechanics
5362:, and the famous
5303:wave interference
5293:, in the form of
5191:described in his
5135:Theory of impetus
5022:quantum tunneling
5017:computer memory.
4975:is the momentum.
4948:
4871:
4868:
4670:
4669:
4667:
4544:and relativistic
4505:
4473:
4443:
4414:
4374:quantum mechanics
4341:
4265:action functional
4248:{\displaystyle V}
3653:
3566:of the particle:
3538:, the total work
3494:
3049:
2826:
2788:
2699:centrifugal force
2600:(informally, the
2367:fictitious forces
2269:
2226:
2182:second derivative
1891:vector quantities
1887:60 − 50 = 10 km/h
1866:
1756:. In cases where
1719:coordinate system
1707:
1706:
1657:dynamic viscosity
1529:moment of inertia
1441:angular position/
1364:quantum mechanics
1338:rely on the same
1308:projectile motion
1218:conservation laws
1214:Noether's theorem
1134:Forces vs. energy
1061:quantum mechanics
943:
942:
690:Centrifugal force
685:Centripetal force
641:Euler's equations
626:Relative velocity
402:Moment of inertia
232:
206:
171:
170:
163:
145:
47:13 September 2024
26:
18:Newtonian physics
16:(Redirected from
7593:
7499:Chemical physics
7439:Particle physics
7365:Classical optics
7248:
7241:
7234:
7225:
7224:
7209:
7104: (monotype)
7068:William Stukeley
7064: (disciple)
7044:Benjamin Pulleyn
7020:Catherine Barton
6939:Newtonian series
6850:Rotating spheres
6596:General Scholium
6491:Sir Isaac Newton
6484:
6477:
6470:
6461:
6460:
6377:Light and Matter
6365:
6346:
6327:
6299:
6278:
6257:
6236:
6209:Kibble, Tom W.B.
6204:
6180:
6161:
6142:Feynman, Richard
6137:
6119:
6118:
6099:Yoder, Joella G.
6095:
6089:
6088:
6070:
6064:
6063:
6045:
6039:
6038:
6020:
6014:
6013:
5993:
5987:
5986:
5958:
5952:
5951:
5935:
5925:
5919:
5916:
5907:
5893:
5887:
5883:
5863:
5857:
5856:
5836:
5830:
5829:
5809:
5803:
5802:
5782:
5776:
5774:
5752:
5746:
5745:
5723:
5717:
5716:
5694:
5688:
5687:
5667:
5661:
5660:
5637:
5631:
5630:
5620:
5611:
5609:
5592:
5586:
5584:
5559:
5543:
5541:
5520:
5512:
5456:Dynamical system
5449:
5444:
5443:
5295:geometric optics
5256:angular momentum
5139:Albert of Saxony
5048:geometric optics
5028:and very narrow
4984:Clinton Davisson
4959:
4957:
4956:
4951:
4949:
4941:
4886:
4884:
4883:
4878:
4872:
4870:
4869:
4867:
4866:
4854:
4849:
4848:
4838:
4837:
4828:
4826:
4825:
4824:
4783:
4767:
4765:
4764:
4759:
4753:
4742:
4685:
4683:
4682:
4677:
4671:
4668:
4666:
4665:
4656:
4655:
4646:
4638:
4637:
4636:
4627:
4622:
4592:. In that case,
4550:Geometric optics
4519:
4517:
4516:
4511:
4506:
4504:
4503:
4494:
4493:
4492:
4482:
4474:
4472:
4468:
4462:
4461:
4456:
4450:
4444:
4442:
4441:
4432:
4431:
4430:
4420:
4415:
4413:
4409:
4403:
4402:
4397:
4391:
4359:
4357:
4356:
4351:
4349:
4348:
4343:
4342:
4334:
4320:. Introduced by
4286:
4284:
4283:
4278:
4254:
4252:
4251:
4246:
4234:
4232:
4231:
4226:
4214:
4212:
4211:
4206:
4179:
4177:
4176:
4171:
4159:
4157:
4156:
4151:
4137:consisting of a
4136:
4134:
4133:
4128:
4070:
4068:
4067:
4062:
4056:
4055:
4054:
4041:
4040:
4039:
3999:
3997:
3996:
3991:
3976:
3975:
3974:
3961:
3960:
3959:
3940:
3939:
3938:
3922:
3921:
3920:
3891:
3889:
3888:
3883:
3877:
3876:
3875:
3856:
3845:
3844:
3843:
3833:
3822:
3811:
3786:
3784:
3783:
3778:
3772:
3771:
3770:
3760:
3749:
3726:potential energy
3716:
3714:
3713:
3708:
3703:
3699:
3697:
3691:
3678:
3672:
3655:
3646:
3640:
3639:
3638:
3637:
3636:
3618:
3617:
3616:
3615:
3614:
3596:
3595:
3594:
3523:
3521:
3520:
3515:
3509:
3508:
3496:
3487:
3481:
3480:
3479:
3401:
3399:
3398:
3393:
3387:
3382:
3371:
3363:
3358:
3357:
3308:
3306:
3305:
3300:
3294:
3283:
3243:potential energy
3175:electromagnetism
3139:
3137:
3136:
3131:
3129:
3128:
3127:
3122:
3117:
3101:
3100:
3095:
3086:
3064:
3062:
3061:
3056:
3050:
3048:
3044:
3038:
3037:
3032:
3026:
3018:
3007:
2979:
2977:
2976:
2971:
2965:
2951:
2950:
2949:
2943:
2912:
2910:
2909:
2904:
2898:
2887:
2872:
2840:
2838:
2837:
2832:
2827:
2825:
2821:
2815:
2811:
2800:
2794:
2789:
2787:
2783:
2777:
2776:
2771:
2765:
2760:
2588:
2586:
2585:
2580:
2578:
2561:
2536:
2511:
2477:
2439:
2432:
2374:reference frames
2357:
2355:
2354:
2349:
2323:reference frames
2283:
2281:
2280:
2275:
2270:
2268:
2267:
2266:
2257:
2251:
2250:
2245:
2244:
2243:
2232:
2227:
2225:
2221:
2215:
2214:
2209:
2203:
2198:
2155:
2153:
2152:
2147:
2129:
2108:
2106:
2105:
2100:
2094:
2071:
2067:
2048:
2046:
2045:
2040:
2034:
2026:
2018:
2017:
1995:
1993:
1992:
1987:
1981:
1973:
1965:
1961:
1925:
1912:
1888:
1879:
1877:
1876:
1871:
1867:
1865:
1861:
1855:
1854:
1849:
1843:
1838:
1680:(weight density)
1549:angular momentum
1463:angular velocity
1430:
1407:
1336:angular momentum
1322:: its position,
1306:The analysis of
1212:. One result is
1166:potential energy
1035:(which includes
935:
928:
921:
908:
903:
902:
895:
891:
890:
796:Johann Bernoulli
791:Daniel Bernoulli
712:Tangential speed
616:
592:
567:Fictitious force
562:
414:Mechanical power
404:
345:Angular momentum
243:
241:
240:
235:
233:
231:
223:
222:
213:
208:
207:
181:
180:
166:
159:
155:
152:
146:
144:
103:
79:
71:
21:
7601:
7600:
7596:
7595:
7594:
7592:
7591:
7590:
7576:
7575:
7574:
7569:
7533:
7519:Medical physics
7470:
7429:Nuclear physics
7398:
7392:Non-equilibrium
7314:
7286:
7258:
7252:
7222:
7217:
7216:
7215:
7214:
7213:
7206:
7193:
7149:Newton's cradle
7130:
7085:
7058: (student)
7056:William Whiston
7052: (student)
7008:
6989:Religious views
6950:
6865:Newton's method
6825:Newtonian fluid
6719:Bucket argument
6705:
6625:
6560:
6493:
6488:
6435:
6386:(uses calculus)
6372:
6362:
6354:. Brooks Cole.
6343:
6324:
6296:
6275:
6254:
6246:. McGraw-Hill.
6233:
6201:
6177:
6167:Six Easy Pieces
6158:
6128:
6126:Further reading
6123:
6122:
6115:
6096:
6092:
6085:
6071:
6067:
6060:
6046:
6042:
6021:
6017:
6010:
5994:
5990:
5959:
5955:
5948:
5926:
5922:
5917:
5910:
5894:
5890:
5880:
5864:
5860:
5853:
5837:
5833:
5826:
5810:
5806:
5799:
5783:
5779:
5771:
5753:
5749:
5742:
5724:
5720:
5713:
5695:
5691:
5684:
5668:
5664:
5657:
5638:
5634:
5621:
5614:
5607:
5593:
5589:
5574:
5560:
5556:
5551:
5546:
5540:
5533:
5522:
5515:
5513:
5509:
5505:
5500:
5445:
5438:
5435:
5277:; however, the
5173:ancient thought
5155:Astronomia nova
5106:and controlled
5073:
5066:
5060:
4969:Planck constant
4940:
4932:
4929:
4928:
4918:
4911:
4896:
4862:
4858:
4853:
4844:
4840:
4839:
4833:
4829:
4827:
4820:
4819:
4815:
4807:
4804:
4803:
4772:
4749:
4738:
4736:
4733:
4732:
4661:
4657:
4651:
4647:
4645:
4632:
4628:
4626:
4618:
4616:
4613:
4612:
4606:
4598:quantum gravity
4530:
4499:
4495:
4488:
4487:
4483:
4481:
4464:
4463:
4457:
4452:
4451:
4449:
4437:
4433:
4426:
4425:
4421:
4419:
4405:
4404:
4398:
4393:
4392:
4390:
4388:
4385:
4384:
4344:
4333:
4332:
4331:
4329:
4326:
4325:
4311:
4305:
4272:
4269:
4268:
4240:
4237:
4236:
4220:
4217:
4216:
4185:
4182:
4181:
4165:
4162:
4161:
4145:
4142:
4141:
4110:
4107:
4106:
4086:
4080:
4050:
4049:
4045:
4035:
4034:
4030:
4019:
4016:
4015:
3970:
3969:
3965:
3955:
3954:
3950:
3934:
3933:
3929:
3916:
3915:
3911:
3903:
3900:
3899:
3871:
3870:
3866:
3852:
3839:
3838:
3834:
3829:
3818:
3807:
3805:
3802:
3801:
3796:
3766:
3765:
3761:
3756:
3745:
3743:
3740:
3739:
3734:
3692:
3687:
3673:
3668:
3663:
3659:
3644:
3632:
3628:
3627:
3626:
3622:
3610:
3606:
3605:
3604:
3600:
3590:
3589:
3585:
3574:
3571:
3570:
3565:
3555:
3548:
3504:
3500:
3485:
3475:
3474:
3470:
3468:
3465:
3464:
3451:
3418:
3411:
3383:
3378:
3367:
3359:
3353:
3349:
3341:
3338:
3337:
3325:
3318:
3290:
3279:
3271:
3268:
3267:
3245:
3233:Main articles:
3231:
3229:Work and energy
3185:exerts a force
3177:. In addition,
3149:
3123:
3118:
3107:
3106:
3102:
3096:
3091:
3090:
3082:
3080:
3077:
3076:
3040:
3039:
3033:
3028:
3027:
3025:
3014:
3003:
2995:
2992:
2991:
2961:
2945:
2944:
2939:
2938:
2936:
2933:
2932:
2894:
2883:
2881:
2878:
2877:
2860:
2851:is called the (
2817:
2816:
2807:
2796:
2795:
2793:
2779:
2778:
2772:
2767:
2766:
2764:
2756:
2754:
2751:
2750:
2721:
2713:Main articles:
2711:
2650:′ is slower by
2576:
2575:
2562:
2554:
2551:
2550:
2537:
2529:
2526:
2525:
2512:
2504:
2501:
2500:
2478:
2470:
2466:
2464:
2461:
2460:
2456:direction, is:
2443:
2434:
2431:
2424:
2422:
2418:
2414:
2410:
2406:
2382:
2334:
2331:
2330:
2327:inertial frames
2311:
2303:Main articles:
2301:
2262:
2258:
2253:
2252:
2246:
2239:
2235:
2234:
2233:
2231:
2217:
2216:
2210:
2205:
2204:
2202:
2194:
2192:
2189:
2188:
2168:
2162:
2122:
2120:
2117:
2116:
2090:
2063:
2062:
2060:
2057:
2056:
2030:
2022:
2010:
2009:
2007:
2004:
2003:
1977:
1969:
1957:
1956:
1954:
1951:
1950:
1914:
1901:
1895:vector analysis
1886:
1857:
1856:
1850:
1845:
1844:
1842:
1834:
1832:
1829:
1828:
1808:
1800:Main articles:
1798:
1678:specific weight
1623:spring constant
1613:surface tension
1511:specific energy
1424:
1417:electromagnetic
1414:
1406:
1400:
1344:rocket equation
1316:point particles
1300:
1230:
1136:
1086:
1081:
952:describing the
950:physical theory
939:
898:
885:
884:
877:
876:
875:
750:
742:
741:
721:
675:Circular motion
669:
659:
658:
657:
614:
584:
581:
560:
539:
531:
530:
527:
526:
484:
474:
466:
465:
464:
423:
419:Mechanical work
412:
396:
334:
326:
325:
324:
279:
271:
248:
224:
218:
214:
212:
203:
202:
200:
197:
196:
167:
156:
150:
147:
104:
102:
92:
80:
67:
60:
55:
54:
53:
52:
51:
50:
34:
22:
15:
12:
11:
5:
7599:
7589:
7588:
7571:
7570:
7568:
7567:
7562:
7557:
7552:
7547:
7541:
7539:
7535:
7534:
7532:
7531:
7526:
7521:
7516:
7511:
7506:
7501:
7496:
7491:
7486:
7480:
7478:
7472:
7471:
7469:
7468:
7463:
7462:
7461:
7456:
7451:
7441:
7436:
7431:
7426:
7425:
7424:
7419:
7408:
7406:
7400:
7399:
7397:
7396:
7395:
7394:
7389:
7382:Thermodynamics
7379:
7378:
7377:
7372:
7362:
7357:
7352:
7351:
7350:
7345:
7340:
7335:
7324:
7322:
7316:
7315:
7313:
7312:
7311:
7310:
7300:
7294:
7292:
7288:
7287:
7285:
7284:
7283:
7282:
7272:
7266:
7264:
7260:
7259:
7251:
7250:
7243:
7236:
7228:
7219:
7218:
7205:
7204:
7202:
7201:
7199:
7195:
7194:
7192:
7191:
7186:
7181:
7176:
7171:
7166:
7161:
7156:
7151:
7146:
7140:
7138:
7132:
7131:
7129:
7128:
7121:
7114:
7105:
7095:
7093:
7087:
7086:
7084:
7083:
7082: (friend)
7077:
7076: (friend)
7071:
7070: (friend)
7065:
7059:
7053:
7047:
7041:
7040: (mentor)
7038:William Clarke
7035:
7029:
7023:
7016:
7014:
7010:
7009:
7007:
7006:
7001:
6996:
6994:Occult studies
6991:
6986:
6981:
6976:
6971:
6965:
6958:
6956:
6952:
6951:
6949:
6948:
6947:
6946:
6936:
6931:
6926:
6921:
6916:
6911:
6910:
6909:
6899:
6894:
6889:
6884:
6879:
6877:Newton fractal
6874:
6873:
6872:
6862:
6857:
6852:
6847:
6842:
6837:
6832:
6827:
6822:
6817:
6812:
6807:
6805:Newton's rings
6802:
6797:
6796:
6795:
6790:
6780:
6775:
6774:
6773:
6763:
6758:
6753:
6752:
6751:
6746:
6741:
6731:
6726:
6721:
6715:
6713:
6707:
6706:
6704:
6703:
6698:
6693:
6691:Newton's metal
6688:
6683:
6678:
6673:
6672:
6671:
6664:Newton polygon
6661:
6656:
6651:
6646:
6645:
6644:
6633:
6631:
6627:
6626:
6624:
6623:
6615:
6607:
6598:" (1713;
6592:
6584:
6577:
6568:
6566:
6565:Other writings
6562:
6561:
6559:
6558:
6550:
6542:
6534:
6526:
6518:
6510:
6501:
6499:
6495:
6494:
6487:
6486:
6479:
6472:
6464:
6458:
6457:
6451:
6445:
6442:e-book library
6430:
6423:
6417:
6411:
6402:
6393:
6387:
6380:
6371:
6370:External links
6368:
6367:
6366:
6360:
6347:
6341:
6328:
6322:
6300:
6294:
6279:
6273:
6258:
6252:
6237:
6231:
6205:
6199:
6181:
6175:
6162:
6156:
6138:
6127:
6124:
6121:
6120:
6113:
6090:
6083:
6065:
6058:
6040:
6015:
6008:
5988:
5969:(3): 197–241.
5953:
5946:
5920:
5908:
5888:
5878:
5858:
5851:
5831:
5824:
5804:
5797:
5777:
5769:
5747:
5740:
5718:
5711:
5689:
5682:
5662:
5655:
5632:
5612:
5605:
5587:
5572:
5553:
5552:
5550:
5547:
5545:
5544:
5538:
5531:
5506:
5504:
5501:
5499:
5498:
5493:
5488:
5483:
5478:
5473:
5468:
5463:
5458:
5452:
5451:
5450:
5447:Physics portal
5434:
5431:
5423:Standard Model
5375:thermodynamics
5299:Newton's rings
5238:law of inertia
5234:laws of motion
5199:laws of motion
5197:the first two
5185:inclined plane
5062:Main article:
5059:
5056:
5003:vacuum chamber
4961:
4960:
4947:
4944:
4939:
4936:
4917:
4914:
4909:
4894:
4888:
4887:
4876:
4865:
4861:
4857:
4852:
4847:
4843:
4836:
4832:
4823:
4818:
4814:
4811:
4769:
4768:
4757:
4752:
4748:
4745:
4741:
4697:its velocity,
4687:
4686:
4675:
4664:
4660:
4654:
4650:
4644:
4641:
4635:
4631:
4625:
4621:
4605:
4602:
4570:thermodynamics
4529:
4526:
4509:
4502:
4498:
4491:
4486:
4480:
4477:
4471:
4467:
4460:
4455:
4447:
4440:
4436:
4429:
4424:
4418:
4412:
4408:
4401:
4396:
4347:
4340:
4337:
4307:Main article:
4304:
4301:
4280:{\textstyle L}
4276:
4244:
4228:{\textstyle T}
4224:
4204:
4201:
4198:
4195:
4192:
4189:
4173:{\textstyle L}
4169:
4153:{\textstyle M}
4149:
4126:
4123:
4120:
4117:
4114:
4082:Main article:
4079:
4076:
4072:
4071:
4060:
4053:
4048:
4044:
4038:
4033:
4029:
4026:
4023:
4001:
4000:
3989:
3985:
3982:
3979:
3973:
3968:
3964:
3958:
3953:
3949:
3946:
3943:
3937:
3932:
3928:
3925:
3919:
3914:
3910:
3907:
3893:
3892:
3881:
3874:
3869:
3865:
3862:
3859:
3855:
3851:
3848:
3842:
3837:
3832:
3828:
3825:
3821:
3817:
3814:
3810:
3794:
3788:
3787:
3776:
3769:
3764:
3759:
3755:
3752:
3748:
3732:
3718:
3717:
3706:
3702:
3696:
3690:
3686:
3682:
3677:
3671:
3667:
3662:
3658:
3652:
3649:
3643:
3635:
3631:
3625:
3621:
3613:
3609:
3603:
3599:
3593:
3588:
3584:
3581:
3578:
3563:
3558:kinetic energy
3553:
3546:
3525:
3524:
3513:
3507:
3503:
3499:
3493:
3490:
3484:
3478:
3473:
3449:
3444:kinetic energy
3431:, as given by
3416:
3409:
3403:
3402:
3391:
3386:
3381:
3377:
3374:
3370:
3366:
3362:
3356:
3352:
3348:
3345:
3323:
3316:
3310:
3309:
3298:
3293:
3289:
3286:
3282:
3278:
3275:
3261:scalar product
3239:kinetic energy
3235:Work (physics)
3230:
3227:
3199:reaction force
3147:
3141:
3140:
3126:
3121:
3116:
3113:
3110:
3105:
3099:
3094:
3089:
3085:
3066:
3065:
3054:
3047:
3043:
3036:
3031:
3024:
3021:
3017:
3013:
3010:
3006:
3002:
2999:
2981:
2980:
2969:
2964:
2960:
2957:
2954:
2948:
2942:
2914:
2913:
2902:
2897:
2893:
2890:
2886:
2842:
2841:
2830:
2824:
2820:
2814:
2810:
2806:
2803:
2799:
2792:
2786:
2782:
2775:
2770:
2763:
2759:
2710:
2707:
2703:Coriolis force
2695:
2694:
2687:speed of light
2683:
2673:
2663:
2642:(the velocity
2622:speed of light
2606:Poincaré group
2590:
2589:
2574:
2571:
2568:
2565:
2563:
2560:
2557:
2553:
2552:
2549:
2546:
2543:
2540:
2538:
2535:
2532:
2528:
2527:
2524:
2521:
2518:
2515:
2513:
2510:
2507:
2503:
2502:
2499:
2496:
2493:
2490:
2487:
2484:
2481:
2479:
2476:
2473:
2469:
2468:
2441:
2429:
2420:
2416:
2412:
2408:
2404:
2380:
2347:
2344:
2341:
2338:
2300:
2297:
2285:
2284:
2273:
2265:
2261:
2256:
2249:
2242:
2238:
2230:
2224:
2220:
2213:
2208:
2201:
2197:
2164:Main article:
2161:
2158:
2157:
2156:
2145:
2141:
2138:
2135:
2132:
2128:
2125:
2110:
2109:
2098:
2093:
2089:
2086:
2083:
2080:
2077:
2074:
2070:
2066:
2050:
2049:
2038:
2033:
2029:
2025:
2021:
2016:
2013:
1997:
1996:
1985:
1980:
1976:
1972:
1968:
1964:
1960:
1882:
1881:
1864:
1860:
1853:
1848:
1841:
1837:
1818:rate of change
1797:
1794:
1715:point particle
1705:
1704:
1701:
1695:
1694:
1691:
1689:number density
1685:
1684:
1681:
1674:
1673:
1670:
1669:(mass density)
1663:
1662:
1659:
1653:
1652:
1649:
1643:
1642:
1639:
1629:
1628:
1625:
1619:
1618:
1615:
1609:
1608:
1605:
1603:energy density
1595:
1594:
1591:
1585:
1584:
1581:
1575:
1574:
1571:
1565:
1564:
1561:
1555:
1554:
1551:
1545:
1544:
1541:
1535:
1534:
1531:
1525:
1524:
1521:
1517:
1516:
1513:
1507:
1506:
1503:
1502:"angular jerk"
1499:
1498:
1495:
1489:
1488:
1485:
1479:
1478:
1475:
1469:
1468:
1465:
1459:
1458:
1455:
1449:
1448:
1445:
1438:
1437:
1434:
1415:(that is, not
1402:Main article:
1399:
1396:
1384:center of mass
1299:
1296:
1295:
1294:
1284:
1270:
1248:
1239:, relating to
1229:
1226:
1162:kinetic energy
1135:
1132:
1104:describes the
1085:
1082:
1080:
1077:
1057:speed of light
1009:Leonhard Euler
941:
940:
938:
937:
930:
923:
915:
912:
911:
910:
909:
896:
879:
878:
874:
873:
868:
863:
858:
853:
848:
843:
838:
833:
828:
823:
818:
813:
808:
803:
798:
793:
788:
783:
778:
773:
768:
763:
758:
752:
751:
748:
747:
744:
743:
740:
739:
720:
719:
714:
709:
704:
702:Coriolis force
699:
698:
697:
687:
682:
677:
671:
670:
665:
664:
661:
660:
656:
655:
650:
645:
644:
643:
638:
628:
623:
618:
611:
600:
599:
598:
593:
580:
579:
574:
569:
564:
557:
552:
547:
541:
540:
537:
536:
533:
532:
529:
528:
525:
524:
519:
514:
509:
504:
499:
493:
487:
485:
478:
475:
472:
471:
468:
467:
463:
462:
457:
452:
447:
442:
437:
432:
427:
421:
416:
410:
405:
394:
389:
384:
379:
374:
373:
372:
367:
357:
352:
347:
342:
336:
335:
332:
331:
328:
327:
323:
322:
317:
312:
307:
302:
297:
292:
287:
281:
280:
277:
276:
273:
272:
270:
269:
264:
259:
253:
250:
249:
244:
230:
227:
221:
217:
211:
193:
192:
186:
185:
169:
168:
83:
81:
74:
58:
36:
30:
27:
25:
9:
6:
4:
3:
2:
7598:
7587:
7584:
7583:
7581:
7566:
7563:
7561:
7558:
7556:
7553:
7551:
7548:
7546:
7543:
7542:
7540:
7536:
7530:
7527:
7525:
7524:Ocean physics
7522:
7520:
7517:
7515:
7512:
7510:
7507:
7505:
7502:
7500:
7497:
7495:
7492:
7490:
7487:
7485:
7482:
7481:
7479:
7477:
7473:
7467:
7464:
7460:
7459:Modern optics
7457:
7455:
7452:
7450:
7447:
7446:
7445:
7442:
7440:
7437:
7435:
7432:
7430:
7427:
7423:
7420:
7418:
7415:
7414:
7413:
7410:
7409:
7407:
7405:
7401:
7393:
7390:
7388:
7385:
7384:
7383:
7380:
7376:
7373:
7371:
7368:
7367:
7366:
7363:
7361:
7358:
7356:
7353:
7349:
7346:
7344:
7341:
7339:
7336:
7334:
7331:
7330:
7329:
7326:
7325:
7323:
7321:
7317:
7309:
7308:Computational
7306:
7305:
7304:
7301:
7299:
7296:
7295:
7293:
7289:
7281:
7278:
7277:
7276:
7273:
7271:
7268:
7267:
7265:
7261:
7257:
7249:
7244:
7242:
7237:
7235:
7230:
7229:
7226:
7212:
7208:
7200:
7196:
7190:
7187:
7185:
7182:
7180:
7177:
7175:
7172:
7170:
7167:
7165:
7162:
7160:
7157:
7155:
7152:
7150:
7147:
7145:
7144:Newton (unit)
7142:
7141:
7139:
7137:
7133:
7127:
7126:
7122:
7120:
7119:
7115:
7112:
7110:
7106:
7103:
7101:
7097:
7096:
7094:
7092:
7088:
7081:
7078:
7075:
7074:William Jones
7072:
7069:
7066:
7063:
7060:
7057:
7054:
7051:
7048:
7046: (tutor)
7045:
7042:
7039:
7036:
7033:
7030:
7027:
7026:John Conduitt
7024:
7022: (niece)
7021:
7018:
7017:
7015:
7011:
7005:
7002:
7000:
6997:
6995:
6992:
6990:
6987:
6985:
6982:
6980:
6977:
6975:
6972:
6969:
6968:Cranbury Park
6966:
6963:
6960:
6959:
6957:
6955:Personal life
6953:
6945:
6942:
6941:
6940:
6937:
6935:
6932:
6930:
6927:
6925:
6922:
6920:
6917:
6915:
6912:
6908:
6905:
6904:
6903:
6902:Newton number
6900:
6898:
6895:
6893:
6890:
6888:
6885:
6883:
6880:
6878:
6875:
6871:
6868:
6867:
6866:
6863:
6861:
6858:
6856:
6853:
6851:
6848:
6846:
6843:
6841:
6838:
6836:
6833:
6831:
6828:
6826:
6823:
6821:
6818:
6816:
6813:
6811:
6808:
6806:
6803:
6801:
6798:
6794:
6791:
6789:
6786:
6785:
6784:
6781:
6779:
6776:
6772:
6771:Kepler's laws
6769:
6768:
6767:
6764:
6762:
6759:
6757:
6754:
6750:
6747:
6745:
6744:parameterized
6742:
6740:
6737:
6736:
6735:
6732:
6730:
6727:
6725:
6722:
6720:
6717:
6716:
6714:
6712:
6708:
6702:
6699:
6697:
6694:
6692:
6689:
6687:
6684:
6682:
6679:
6677:
6674:
6670:
6667:
6666:
6665:
6662:
6660:
6657:
6655:
6652:
6650:
6647:
6643:
6640:
6639:
6638:
6635:
6634:
6632:
6630:Contributions
6628:
6621:
6620:
6616:
6613:
6612:
6608:
6605:
6603:
6597:
6593:
6590:
6589:
6585:
6583:" (1675)
6582:
6578:
6575:
6574:
6570:
6569:
6567:
6563:
6556:
6555:
6551:
6548:
6547:
6543:
6540:
6539:
6535:
6532:
6531:
6527:
6524:
6523:
6519:
6516:
6515:
6511:
6508:
6507:
6503:
6502:
6500:
6496:
6492:
6485:
6480:
6478:
6473:
6471:
6466:
6465:
6462:
6456:
6452:
6449:
6446:
6443:
6439:
6434:
6431:
6428:
6425:Tong, David.
6424:
6422:
6418:
6416:
6412:
6409:
6408:
6403:
6400:
6399:
6394:
6392:
6388:
6385:
6381:
6378:
6374:
6373:
6363:
6357:
6353:
6348:
6344:
6338:
6335:. CRC Press.
6334:
6329:
6325:
6319:
6316:. MIT Press.
6315:
6314:
6309:
6305:
6301:
6297:
6291:
6287:
6286:
6280:
6276:
6270:
6266:
6265:
6259:
6255:
6249:
6245:
6244:
6238:
6234:
6228:
6224:
6220:
6219:
6214:
6210:
6206:
6202:
6196:
6192:
6191:
6186:
6182:
6178:
6172:
6168:
6163:
6159:
6153:
6149:
6148:
6143:
6139:
6135:
6130:
6129:
6116:
6110:
6106:
6105:
6100:
6094:
6086:
6084:9781107015463
6080:
6076:
6069:
6061:
6055:
6051:
6044:
6036:
6032:
6028:
6027:
6019:
6011:
6009:9780521575720
6005:
6001:
6000:
5992:
5984:
5980:
5976:
5972:
5968:
5964:
5957:
5949:
5943:
5939:
5934:
5933:
5924:
5915:
5913:
5905:
5901:
5897:
5892:
5886:
5881:
5875:
5871:
5870:
5862:
5854:
5852:0-486-65067-7
5848:
5844:
5843:
5835:
5827:
5825:0-486-69690-1
5821:
5817:
5816:
5808:
5800:
5794:
5790:
5789:
5781:
5772:
5766:
5762:
5758:
5751:
5743:
5737:
5733:
5729:
5722:
5714:
5708:
5704:
5700:
5693:
5685:
5683:0-89116-355-7
5679:
5675:
5674:
5666:
5658:
5656:0-521-35883-3
5652:
5648:
5647:
5642:
5636:
5628:
5627:
5619:
5617:
5608:
5602:
5598:
5591:
5583:
5579:
5575:
5573:0-7546-4091-4
5569:
5565:
5558:
5554:
5537:
5530:
5526:
5519:
5511:
5507:
5497:
5494:
5492:
5489:
5487:
5484:
5482:
5479:
5477:
5474:
5472:
5469:
5467:
5464:
5462:
5459:
5457:
5454:
5453:
5448:
5442:
5437:
5430:
5428:
5424:
5419:
5414:
5412:
5408:
5404:
5401:and sizes of
5400:
5399:energy levels
5396:
5392:
5388:
5384:
5381:of classical
5380:
5379:Gibbs paradox
5376:
5371:
5369:
5365:
5361:
5353:
5349:
5345:
5341:
5337:
5335:
5331:
5322:
5318:
5314:
5310:
5308:
5304:
5300:
5296:
5292:
5288:
5284:
5280:
5276:
5271:
5269:
5268:Kepler's laws
5265:
5261:
5257:
5253:
5249:
5248:
5243:
5239:
5235:
5227:
5223:
5218:
5214:
5212:
5208:
5204:
5200:
5196:
5195:
5190:
5186:
5182:
5181:tower of Pisa
5178:
5174:
5170:
5166:
5162:
5158:
5156:
5151:
5147:
5140:
5137:according to
5136:
5131:
5127:
5125:
5121:
5117:
5113:
5109:
5105:
5101:
5098:, founder of
5097:
5093:
5088:
5086:
5082:
5078:
5071:
5065:
5055:
5053:
5049:
5045:
5040:
5038:
5034:
5031:
5027:
5026:tunnel diodes
5023:
5018:
5016:
5012:
5008:
5004:
5000:
4996:
4993:
4989:
4988:Lester Germer
4985:
4981:
4976:
4974:
4970:
4966:
4945:
4942:
4937:
4934:
4927:
4926:
4925:
4923:
4913:
4908:
4904:
4900:
4893:
4874:
4863:
4859:
4855:
4850:
4845:
4841:
4834:
4830:
4816:
4812:
4809:
4802:
4801:
4800:
4798:
4794:
4790:
4785:
4782:
4779:
4775:
4755:
4746:
4743:
4731:
4730:
4729:
4727:
4723:
4719:
4715:
4710:
4708:
4704:
4700:
4696:
4692:
4673:
4662:
4658:
4652:
4648:
4642:
4639:
4629:
4623:
4611:
4610:
4609:
4601:
4599:
4595:
4591:
4587:
4583:
4579:
4575:
4571:
4566:
4562:
4557:
4555:
4551:
4547:
4543:
4534:
4525:
4523:
4507:
4478:
4475:
4469:
4445:
4416:
4410:
4382:
4377:
4375:
4371:
4367:
4363:
4345:
4338:
4335:
4323:
4319:
4315:
4310:
4300:
4298:
4294:
4290:
4274:
4266:
4262:
4258:
4242:
4222:
4202:
4199:
4196:
4193:
4190:
4187:
4167:
4147:
4140:
4121:
4118:
4115:
4104:
4103:
4098:
4094:
4090:
4085:
4075:
4058:
4046:
4042:
4031:
4027:
4024:
4021:
4014:
4013:
4012:
4010:
4006:
3987:
3983:
3980:
3966:
3962:
3951:
3930:
3923:
3912:
3905:
3898:
3897:
3896:
3879:
3867:
3860:
3857:
3846:
3835:
3826:
3823:
3812:
3800:
3799:
3798:
3793:
3774:
3762:
3753:
3750:
3738:
3737:
3736:
3731:
3727:
3723:
3704:
3700:
3694:
3688:
3684:
3680:
3675:
3669:
3665:
3660:
3656:
3650:
3647:
3641:
3633:
3623:
3619:
3611:
3601:
3597:
3586:
3579:
3576:
3569:
3568:
3567:
3562:
3559:
3552:
3545:
3541:
3537:
3533:
3528:
3511:
3505:
3501:
3497:
3491:
3488:
3482:
3471:
3463:
3462:
3461:
3459:
3455:
3448:
3445:
3440:
3438:
3434:
3430:
3426:
3422:
3415:
3408:
3389:
3375:
3354:
3350:
3346:
3343:
3336:
3335:
3334:
3333:
3332:line integral
3329:
3326:along a path
3322:
3315:
3296:
3284:
3276:
3273:
3266:
3265:
3264:
3262:
3258:
3254:
3250:
3244:
3240:
3236:
3226:
3224:
3220:
3216:
3212:
3208:
3204:
3200:
3196:
3192:
3188:
3184:
3180:
3176:
3172:
3171:Lorentz force
3168:
3163:
3161:
3157:
3153:
3146:
3124:
3119:
3114:
3111:
3108:
3103:
3097:
3087:
3075:
3074:
3073:
3071:
3052:
3045:
3022:
3019:
3011:
3008:
3000:
2997:
2990:
2989:
2988:
2986:
2967:
2958:
2955:
2952:
2931:
2930:
2929:
2926:
2924:
2920:
2900:
2891:
2888:
2876:
2875:
2874:
2871:
2867:
2863:
2858:
2854:
2850:
2847:
2844:The quantity
2828:
2822:
2804:
2790:
2784:
2761:
2749:
2748:
2747:
2744:
2740:
2736:
2732:
2728:
2726:
2720:
2716:
2706:
2704:
2700:
2692:
2688:
2684:
2681:
2677:
2674:
2671:
2667:
2664:
2661:
2657:
2653:
2649:
2645:
2641:
2637:
2633:
2630:
2629:
2628:
2625:
2623:
2619:
2615:
2611:
2607:
2603:
2599:
2596:known as the
2595:
2572:
2569:
2566:
2564:
2558:
2555:
2547:
2544:
2541:
2539:
2533:
2530:
2522:
2519:
2516:
2514:
2508:
2505:
2497:
2494:
2491:
2488:
2485:
2482:
2480:
2474:
2471:
2459:
2458:
2457:
2455:
2451:
2447:
2437:
2427:
2402:
2398:
2394:
2390:
2386:
2378:
2375:
2372:Consider two
2370:
2368:
2363:
2359:
2345:
2342:
2339:
2336:
2328:
2324:
2320:
2316:
2310:
2306:
2296:
2294:
2290:
2271:
2263:
2259:
2240:
2228:
2222:
2199:
2187:
2186:
2185:
2183:
2179:
2175:
2174:
2167:
2143:
2139:
2136:
2133:
2130:
2126:
2123:
2115:
2114:
2113:
2096:
2084:
2081:
2078:
2072:
2068:
2055:
2054:
2053:
2036:
2027:
2019:
2014:
2002:
2001:
2000:
1983:
1974:
1966:
1962:
1949:
1948:
1947:
1945:
1941:
1937:
1933:
1929:
1924:
1921:
1917:
1911:
1908:
1904:
1898:
1896:
1892:
1862:
1839:
1827:
1826:
1825:
1823:
1819:
1815:
1814:
1807:
1803:
1793:
1791:
1787:
1786:absolute time
1783:
1782:time interval
1779:
1775:
1771:
1767:
1763:
1759:
1755:
1751:
1747:
1743:
1739:
1735:
1732:
1728:
1724:
1720:
1716:
1712:
1702:
1700:
1697:
1696:
1692:
1690:
1687:
1686:
1682:
1679:
1676:
1675:
1671:
1668:
1665:
1664:
1660:
1658:
1655:
1654:
1650:
1648:
1645:
1644:
1640:
1638:
1634:
1631:
1630:
1626:
1624:
1621:
1620:
1616:
1614:
1611:
1610:
1606:
1604:
1600:
1597:
1596:
1592:
1590:
1587:
1586:
1582:
1580:
1577:
1576:
1572:
1570:
1567:
1566:
1562:
1560:
1557:
1556:
1552:
1550:
1547:
1546:
1542:
1540:
1537:
1536:
1532:
1530:
1527:
1526:
1522:
1519:
1518:
1514:
1512:
1509:
1508:
1504:
1501:
1500:
1496:
1494:
1491:
1490:
1486:
1484:
1481:
1480:
1476:
1474:
1471:
1470:
1466:
1464:
1461:
1460:
1456:
1454:
1451:
1450:
1446:
1444:
1440:
1439:
1435:
1432:
1431:
1428:
1422:
1418:
1412:
1405:
1395:
1393:
1387:
1385:
1381:
1377:
1373:
1369:
1365:
1361:
1357:
1353:
1348:
1345:
1341:
1337:
1333:
1329:
1325:
1321:
1317:
1309:
1304:
1292:
1291:thermodynamic
1288:
1285:
1282:
1278:
1274:
1271:
1268:
1264:
1260:
1256:
1252:
1249:
1246:
1242:
1238:
1235:
1234:
1233:
1225:
1223:
1219:
1215:
1211:
1207:
1203:
1199:
1195:
1191:
1187:
1183:
1179:
1175:
1171:
1167:
1163:
1159:
1158:
1153:
1150:In contrast,
1148:
1146:
1142:
1131:
1129:
1125:
1124:
1119:
1115:
1111:
1107:
1103:
1102:
1097:
1093:
1092:
1076:
1074:
1070:
1066:
1062:
1058:
1053:
1049:
1044:
1042:
1038:
1034:
1030:
1026:
1022:
1018:
1014:
1010:
1006:
1002:
998:
993:
991:
987:
983:
979:
975:
971:
967:
963:
959:
955:
951:
947:
936:
931:
929:
924:
922:
917:
916:
914:
913:
907:
897:
894:
889:
883:
882:
881:
880:
872:
869:
867:
864:
862:
859:
857:
854:
852:
849:
847:
844:
842:
839:
837:
834:
832:
829:
827:
824:
822:
819:
817:
814:
812:
809:
807:
804:
802:
799:
797:
794:
792:
789:
787:
784:
782:
779:
777:
774:
772:
769:
767:
764:
762:
759:
757:
754:
753:
746:
745:
738:
734:
730:
726:
723:
722:
718:
715:
713:
710:
708:
705:
703:
700:
696:
693:
692:
691:
688:
686:
683:
681:
678:
676:
673:
672:
668:
663:
662:
654:
651:
649:
646:
642:
639:
637:
634:
633:
632:
629:
627:
624:
622:
619:
617:
612:
609:
605:
602:
601:
597:
594:
591:
587:
583:
582:
578:
575:
573:
570:
568:
565:
563:
558:
556:
553:
551:
548:
546:
543:
542:
535:
534:
523:
520:
518:
515:
513:
510:
508:
505:
503:
500:
498:
495:
494:
492:
491:
486:
483:
482:
477:
476:
470:
469:
461:
458:
456:
453:
451:
448:
446:
443:
441:
438:
436:
433:
431:
428:
426:
422:
420:
417:
415:
411:
409:
406:
403:
399:
395:
393:
390:
388:
385:
383:
380:
378:
375:
371:
368:
366:
363:
362:
361:
358:
356:
353:
351:
348:
346:
343:
341:
338:
337:
330:
329:
321:
318:
316:
313:
311:
308:
306:
303:
301:
298:
296:
293:
291:
288:
286:
283:
282:
275:
274:
268:
265:
263:
260:
258:
255:
254:
252:
251:
247:
228:
225:
215:
209:
195:
194:
191:
188:
187:
183:
182:
175:
165:
162:
154:
143:
140:
136:
133:
129:
126:
122:
119:
115:
112: –
111:
107:
106:Find sources:
100:
96:
90:
89:
84:This article
82:
78:
73:
72:
69:
65:
48:
44:
40:
33:
28:
19:
7484:Astrophysics
7327:
7298:Experimental
7211:Isaac Newton
7123:
7116:
7108:
7099:
7032:Isaac Barrow
6970: (home)
6829:
6711:Newtonianism
6686:Newton scale
6649:Impact depth
6622: (1754)
6617:
6614: (1728)
6609:
6599:
6586:
6571:
6557: (1711)
6552:
6549: (1707)
6544:
6541: (1704)
6536:
6533: (1704)
6528:
6525: (1687)
6520:
6517: (1684)
6512:
6509: (1671)
6504:
6498:Publications
6405:
6396:
6351:
6332:
6312:
6284:
6263:
6242:
6217:
6189:
6166:
6146:
6133:
6103:
6093:
6074:
6068:
6049:
6043:
6025:
6018:
5998:
5991:
5966:
5962:
5956:
5931:
5923:
5891:
5868:
5861:
5841:
5834:
5814:
5807:
5787:
5780:
5760:
5757:"Kinematics"
5750:
5731:
5721:
5702:
5692:
5672:
5665:
5644:
5635:
5625:
5596:
5590:
5563:
5557:
5535:
5528:
5524:
5517:
5510:
5415:
5372:
5357:
5326:
5278:
5272:
5245:
5231:
5222:Isaac Newton
5192:
5153:
5143:
5133:Three stage
5111:
5089:
5074:
5041:
5019:
4977:
4972:
4964:
4962:
4919:
4906:
4898:
4891:
4889:
4799:is given by
4786:
4780:
4777:
4773:
4770:
4725:
4721:
4717:
4713:
4711:
4706:
4702:
4698:
4694:
4690:
4688:
4607:
4558:
4539:
4378:
4361:
4312:
4100:
4087:
4073:
4004:
4002:
3894:
3791:
3789:
3729:
3728:and denoted
3719:
3560:
3550:
3543:
3539:
3535:
3529:
3526:
3460:is given by
3457:
3453:
3446:
3441:
3421:conservative
3413:
3406:
3404:
3327:
3320:
3313:
3311:
3256:
3252:
3248:
3246:
3222:
3218:
3214:
3210:
3206:
3202:
3198:
3194:
3190:
3186:
3182:
3164:
3159:
3144:
3142:
3068:This can be
3067:
2984:
2982:
2927:
2922:
2915:
2869:
2865:
2861:
2848:
2845:
2843:
2729:
2722:
2696:
2679:
2675:
2669:
2665:
2659:
2655:
2651:
2647:
2643:
2639:
2635:
2631:
2626:
2617:
2613:
2601:
2591:
2453:
2449:
2445:
2435:
2425:
2400:
2396:
2392:
2388:
2384:
2376:
2371:
2360:
2358:, is valid.
2312:
2293:deceleration
2292:
2288:
2286:
2173:acceleration
2171:
2169:
2166:Acceleration
2160:Acceleration
2111:
2051:
1998:
1944:unit vectors
1939:
1935:
1931:
1927:
1922:
1919:
1915:
1909:
1906:
1902:
1899:
1883:
1811:
1809:
1769:
1765:
1761:
1757:
1753:
1749:
1745:
1741:
1733:
1726:
1710:
1708:
1473:acceleration
1388:
1355:
1349:
1332:Euler's laws
1313:
1231:
1155:
1149:
1137:
1122:
1099:
1089:
1087:
1052:Chaos theory
1045:
1001:Isaac Newton
994:
985:
945:
944:
735: /
731: /
729:displacement
727: /
588: /
550:Displacement
488:
479:
473:Formulations
460:Virtual work
400: /
340:Acceleration
333:Fundamentals
189:
157:
148:
138:
131:
124:
117:
105:
93:Please help
88:verification
85:
68:
46:
37:This is the
31:
7387:Statistical
7303:Theoretical
7280:Engineering
7111:by Paolozzi
7050:Roger Cotes
6659:Newton disc
6573:Quaestiones
6546:Arithmetica
6308:Jack Wisdom
5385:, in which
5350:now called
5161:Tycho Brahe
5081:engineering
5011:milliradian
4992:diffraction
3433:Hooke's law
2419:) in frame
2399:) in frame
1637:energy flux
1190:phase space
1118:mathematics
1108:of points,
1096:equilibrium
960:, parts of
958:projectiles
871:von Neumann
538:Core topics
7504:Geophysics
7494:Biophysics
7338:Analytical
7291:Approaches
7198:Categories
7174:XMM-Newton
7091:Depictions
7062:John Keill
6984:Apple tree
6979:Later life
6974:Early life
6554:De Analysi
5673:Kinematics
5549:References
5108:experiment
5085:technology
5030:transistor
3072:to obtain
3070:integrated
2178:derivative
1822:derivative
1633:irradiance
1404:Kinematics
1398:Kinematics
1370:, e.g., a
1326:, and the
1320:parameters
1222:symmetries
1147:quantity.
1101:Kinematics
966:spacecraft
806:d'Alembert
786:Maupertuis
749:Scientists
631:Rigid body
305:Kinematics
121:newspapers
7454:Molecular
7355:Acoustics
7348:Continuum
7343:Celestial
7333:Newtonian
7320:Classical
7263:Divisions
7013:Relations
6522:Principia
5279:Principia
5096:Aristotle
5052:rest mass
4995:side lobe
4980:electrons
4935:λ
4797:magnetron
4789:cyclotron
4744:≈
4643:−
4497:∂
4485:∂
4479:−
4435:∂
4423:∂
4339:˙
4261:potential
4197:−
4022:∑
3945:Δ
3942:⇒
3927:Δ
3909:Δ
3906:−
3864:Δ
3861:−
3850:Δ
3847:⋅
3831:∇
3827:−
3816:Δ
3813:⋅
3758:∇
3754:−
3681:−
3620:−
3583:Δ
3376:⋅
3351:∫
3288:Δ
3285:⋅
3257:work done
3112:λ
3109:−
3001:λ
2998:−
2959:λ
2956:−
2853:canonical
2489:−
2137:−
2082:−
2028:−
1975:−
1816:, or the
1748:to point
1380:composite
1174:variation
986:classical
962:machinery
851:Liouville
733:frequency
653:Vibration
370:potential
295:Continuum
290:Celestial
267:Textbooks
151:July 2022
7580:Category
7136:Namesake
7102:by Blake
6696:Spectrum
6637:Calculus
6606: )
6506:Fluxions
6310:(2001).
6215:(2004).
6144:(1999).
6101:(1988).
6035:68159539
5983:41133689
5900:Archived
5643:(1904).
5582:53887772
5433:See also
5405:and the
5344:Hamilton
5317:Lagrange
5275:calculus
5169:ellipses
4793:gyrotron
4574:velocity
4255:are the
3722:gradient
3437:friction
3169:and the
2857:momentum
2739:momentum
2608:used in
2559:′
2534:′
2509:′
2475:′
2319:observer
2315:particle
2127:′
2069:′
2015:′
1963:′
1926:, where
1813:velocity
1802:Velocity
1731:particle
1711:position
1599:pressure
1539:momentum
1453:velocity
1433:position
1372:baseball
1360:electron
1352:non-zero
1340:calculus
1123:Dynamics
1079:Branches
978:galaxies
906:Category
831:Hamilton
816:Lagrange
811:Clairaut
776:Horrocks
737:velocity
707:Pendulum
695:reactive
667:Rotation
636:dynamics
586:Inertial
572:Friction
455:Velocity
430:Momentum
310:Kinetics
300:Dynamics
278:Branches
262:Timeline
43:reviewed
7538:Related
7422:General
7417:Special
7275:Applied
6654:Inertia
6642:fluxion
6538:Queries
6530:Opticks
6514:De Motu
5539:initial
5418:physics
5387:entropy
5287:Huygens
5260:gravity
5177:Galileo
5150:planets
5120:gravity
5077:science
5058:History
4999:crystal
4967:is the
4905:) mass
4362:momenta
4293:minimum
4289:maximum
4257:kinetic
3425:Gravity
2452:in the
1736:with a
1703:kg·m·s
1683:kg·m·s
1667:density
1661:kg·m·s
1607:kg·m·s
1593:kg·m·s
1583:kg·m·s
1573:kg·m·s
1563:kg·m·s
1553:kg·m·s
1543:kg·m·s
1421:thermal
1281:general
1277:special
1263:liquids
1261:(i.e.,
1245:planets
1091:Statics
970:planets
866:Koopman
826:Poisson
821:Laplace
766:Huygens
761:Galileo
606: (
545:Damping
398:Inertia
392:Impulse
365:kinetic
315:Statics
285:Applied
257:History
135:scholar
7449:Atomic
7404:Modern
7254:Major
7109:Newton
7100:Newton
6358:
6339:
6320:
6292:
6271:
6250:
6229:
6197:
6173:
6154:
6111:
6081:
6056:
6033:
6006:
5981:
5944:
5876:
5849:
5822:
5795:
5767:
5738:
5709:
5680:
5653:
5603:
5580:
5570:
5395:quanta
5283:Euclid
5236:: the
5146:causal
5124:forces
5104:theory
5083:, and
4963:where
4890:where
4705:, and
4689:where
4297:saddle
4215:where
4009:energy
3429:spring
3255:, the
3241:, and
3143:where
2983:where
2731:Newton
2620:, the
1738:vector
1699:action
1579:energy
1569:torque
1328:forces
1259:fluids
1255:solids
1204:, and
1184:, and
1168:. The
1157:scalar
1145:vector
1114:forces
1110:bodies
1106:motion
1021:energy
1017:forces
1013:bodies
976:, and
954:motion
904:
856:Appell
841:Cauchy
836:Jacobi
781:Halley
771:Newton
756:Kepler
608:linear
604:Motion
450:Torque
425:Moment
360:Energy
350:Couple
137:
130:
123:
116:
108:
6944:table
5979:JSTOR
5532:final
5503:Notes
5403:atoms
5291:light
5090:Some
5033:gates
4901:and (
4295:, or
3213:and −
3205:, on
2735:force
2725:field
2715:Force
2685:the
2433:when
2403:and (
1806:speed
1723:space
1713:of a
1672:kg·m
1641:kg·s
1627:kg·s
1617:kg·s
1589:power
1559:force
1533:kg·m
1443:angle
1267:gases
1241:stars
1154:uses
974:stars
948:is a
861:Gibbs
846:Routh
801:Euler
440:Speed
435:Space
377:Force
142:JSTOR
128:books
7375:Wave
7270:Pure
6356:ISBN
6337:ISBN
6318:ISBN
6290:ISBN
6269:ISBN
6248:ISBN
6227:ISBN
6195:ISBN
6171:ISBN
6152:ISBN
6109:ISBN
6079:ISBN
6054:ISBN
6031:OCLC
6004:ISBN
5942:ISBN
5874:ISBN
5847:ISBN
5820:ISBN
5793:ISBN
5765:ISBN
5736:ISBN
5707:ISBN
5678:ISBN
5651:ISBN
5601:ISBN
5578:OCLC
5568:ISBN
5254:and
5220:Sir
5165:Mars
4986:and
4971:and
4903:rest
4368:and
4259:and
4235:and
3530:The
3442:The
3221:and
3173:for
2737:and
2717:and
2701:and
2678:′ =
2668:′ =
2634:′ =
2444:and
2379:and
2307:and
2170:The
1942:are
1938:and
1810:The
1804:and
1774:time
1709:The
1651:m·s
1635:and
1601:and
1523:m·s
1515:m·s
1497:m·s
1493:jerk
1477:m·s
1457:m·s
1409:The
1376:spin
1374:can
1356:very
1324:mass
1279:and
1265:and
1257:and
1164:and
1039:and
445:Time
408:Mass
114:news
7370:Ray
5971:doi
5301:(a
5262:in
5213:.
5046:as
5035:in
5024:in
4712:If
3549:to
3412:to
3319:to
3201:, −
2864:= d
2438:= 0
1419:or
1394:).
97:by
45:on
7582::
6401:".
6306:;
6225:.
6221:.
6211:;
5977:.
5967:28
5965:.
5940:.
5938:50
5911:^
5898:.
5759:.
5730:.
5701:.
5615:^
5576:,
5534:−
5527:=
5413:.
5336:.
5309:.
5126:.
5079:,
5039:.
4791:,
4776:=
4720:,
4548:.
4376:.
4291:,
4011:,
3735::
3423:.
3237:,
2925:.
2868:/d
2855:)
2705:.
2638:−
2624:.
2442:S'
2430:x'
2428:=
2421:S'
2417:t'
2413:z'
2409:y'
2405:x'
2381:S'
1918:=
1905:=
1897:.
1772:,
1764:,
1693:m
1505:s
1487:s
1467:s
1436:m
1411:SI
1269:).
1243:,
1224:.
1200:,
1120:.
1027:,
1007:,
972:,
968:,
964:,
41:,
7247:e
7240:t
7233:v
6604:"
6600:"
6594:"
6579:"
6483:e
6476:t
6469:v
6364:.
6345:.
6326:.
6298:.
6277:.
6256:.
6235:.
6203:.
6179:.
6160:.
6117:.
6087:.
6062:.
6037:.
6012:.
5985:.
5973::
5950:.
5882:.
5855:.
5828:.
5801:.
5775:.
5773:.
5744:.
5715:.
5686:.
5659:.
5610:.
5585:.
5542:.
5536:r
5529:r
5525:r
5523:Δ
5518:r
5516:Δ
5354:.
5323:.
5157:,
5072:.
4973:p
4965:h
4946:p
4943:h
4938:=
4910:0
4907:m
4899:T
4895:c
4892:f
4875:,
4864:2
4860:c
4856:T
4851:+
4846:0
4842:m
4835:0
4831:m
4822:c
4817:f
4813:=
4810:f
4781:v
4778:m
4774:p
4756:.
4751:v
4747:m
4740:p
4726:c
4724:/
4722:v
4718:c
4714:v
4707:c
4703:v
4699:v
4695:v
4691:m
4674:,
4663:2
4659:c
4653:2
4649:v
4640:1
4634:v
4630:m
4624:=
4620:p
4508:.
4501:q
4490:H
4476:=
4470:t
4466:d
4459:p
4454:d
4446:,
4439:p
4428:H
4417:=
4411:t
4407:d
4400:q
4395:d
4346:i
4336:q
4275:L
4243:V
4223:T
4203:,
4200:V
4194:T
4191:=
4188:L
4168:L
4148:M
4125:)
4122:L
4119:,
4116:M
4113:(
4059:,
4052:p
4047:E
4043:+
4037:k
4032:E
4028:=
4025:E
3988:.
3984:0
3981:=
3978:)
3972:p
3967:E
3963:+
3957:k
3952:E
3948:(
3936:k
3931:E
3924:=
3918:p
3913:E
3880:.
3873:p
3868:E
3858:=
3854:r
3841:p
3836:E
3824:=
3820:r
3809:F
3795:p
3792:E
3775:.
3768:p
3763:E
3751:=
3747:F
3733:p
3730:E
3705:.
3701:)
3695:2
3689:1
3685:v
3676:2
3670:2
3666:v
3661:(
3657:m
3651:2
3648:1
3642:=
3634:1
3630:k
3624:E
3612:2
3608:k
3602:E
3598:=
3592:k
3587:E
3580:=
3577:W
3564:k
3561:E
3554:2
3551:r
3547:1
3544:r
3540:W
3536:m
3512:.
3506:2
3502:v
3498:m
3492:2
3489:1
3483:=
3477:k
3472:E
3458:v
3454:m
3450:k
3447:E
3417:2
3414:r
3410:1
3407:r
3390:.
3385:r
3380:d
3373:)
3369:r
3365:(
3361:F
3355:C
3347:=
3344:W
3328:C
3324:2
3321:r
3317:1
3314:r
3297:.
3292:r
3281:F
3277:=
3274:W
3253:r
3249:F
3223:B
3219:A
3215:F
3211:F
3207:A
3203:F
3195:B
3191:B
3187:F
3183:A
3160:r
3148:0
3145:v
3125:m
3120:/
3115:t
3104:e
3098:0
3093:v
3088:=
3084:v
3053:.
3046:t
3042:d
3035:v
3030:d
3023:m
3020:=
3016:a
3012:m
3009:=
3005:v
2985:λ
2968:,
2963:v
2953:=
2947:R
2941:F
2901:.
2896:a
2892:m
2889:=
2885:F
2870:t
2866:v
2862:a
2849:v
2846:m
2829:.
2823:t
2819:d
2813:)
2809:v
2805:m
2802:(
2798:d
2791:=
2785:t
2781:d
2774:p
2769:d
2762:=
2758:F
2680:F
2676:F
2670:a
2666:a
2662:)
2660:S
2656:v
2652:u
2648:S
2644:v
2640:u
2636:v
2632:v
2618:c
2614:u
2573:.
2570:t
2567:=
2556:t
2548:,
2545:z
2542:=
2531:z
2523:,
2520:y
2517:=
2506:y
2498:,
2495:u
2492:t
2486:x
2483:=
2472:x
2454:x
2450:u
2446:S
2436:t
2426:x
2415:,
2411:,
2407:,
2401:S
2397:t
2395:,
2393:z
2391:,
2389:y
2387:,
2385:x
2377:S
2346:a
2343:m
2340:=
2337:F
2289:v
2272:.
2264:2
2260:t
2255:d
2248:r
2241:2
2237:d
2229:=
2223:t
2219:d
2212:v
2207:d
2200:=
2196:a
2144:.
2140:v
2134:u
2131:=
2124:u
2097:.
2092:d
2088:)
2085:v
2079:u
2076:(
2073:=
2065:u
2037:.
2032:u
2024:v
2020:=
2012:v
1984:.
1979:v
1971:u
1967:=
1959:u
1940:e
1936:d
1932:v
1928:u
1923:e
1920:v
1916:v
1910:d
1907:u
1903:u
1880:.
1863:t
1859:d
1852:r
1847:d
1840:=
1836:v
1770:t
1766:r
1762:O
1758:P
1754:O
1750:P
1746:O
1742:r
1734:P
1727:O
1427:s
1423:)
934:e
927:t
920:v
610:)
229:t
226:d
220:p
216:d
210:=
205:F
164:)
158:(
153:)
149:(
139:·
132:·
125:·
118:·
91:.
66:.
49:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
