4540:
734:
1015:. The figure shows a man on top of a train, at the back edge. At 1:00 pm he begins to walk forward at a walking speed of 10 km/h (kilometers per hour). The train is moving at 40 km/h. The figure depicts the man and train at two different times: first, when the journey began, and also one hour later at 2:00 pm. The figure suggests that the man is 50 km from the starting point after having traveled (by walking and by train) for one hour. This, by definition, is 50 km/h, which suggests that the prescription for calculating relative velocity in this fashion is to add the two velocities.
20:
747:
1311:
4576:
4600:
4552:
4588:
4564:
4238:
1678:
3235:
3088:
1153:
3942:
4040:
3609:
3374:
1529:
2664:
2946:
3103:
2962:
4029:
3461:
1036:
3672:
1942:
2022:
4233:{\displaystyle v_{\mathrm {B|A} }={\sqrt {1-{\frac {\left(c^{2}-v_{\mathrm {A} }^{2}\right)\left(c^{2}-v_{\mathrm {B} }^{2}\right)}{\left(c^{2}-\mathbf {v} _{\mathrm {A} }\cdot \mathbf {v} _{\mathrm {B} }\right)^{2}}}}}\cdot c}
2806:
1752:
1466:
1395:
3472:
1673:{\displaystyle \mathbf {r} _{B}-\mathbf {r} _{A}=\underbrace {\mathbf {r} _{Bi}-\mathbf {r} _{Ai}} _{\text{initial separation}}+\underbrace {(\mathbf {v} _{B}-\mathbf {v} _{A})t} _{\text{relative velocity}}.}
4362:
2282:
3290:
88:
980:
2118:
where x' is the position as seen by a reference frame that is moving at speed, v, in the "unprimed" (x) reference frame. Taking the differential of the first of the two equations above, we have,
898:
1859:
1807:
1298:
Fully legitimate expressions for "the velocity of A relative to B" include "the velocity of A with respect to B" and "the velocity of A in the coordinate system where B is always at rest". The
1521:
2829:
2956:
In the case where two objects are traveling in parallel directions, the relativistic formula for relative velocity is similar in form to the formula for addition of relativistic velocities.
1018:
The diagram displays clocks and rulers to remind the reader that while the logic behind this calculation seem flawless, it makes false assumptions about how clocks and rulers behave. (See
3656:
3282:
3230:{\displaystyle v_{\mathrm {B|A} }={\frac {\left|\mathbf {v} _{\mathrm {B} }-\mathbf {v} _{\mathrm {A} }\right|}{1-{\frac {\mathbf {v} _{\mathrm {A} }\mathbf {v} _{\mathrm {B} }}{c^{2}}}}}}
2724:
2413:
3083:{\displaystyle \mathbf {v} _{\mathrm {B|A} }={\frac {\mathbf {v} _{\mathrm {B} }-\mathbf {v} _{\mathrm {A} }}{1-{\frac {\mathbf {v} _{\mathrm {A} }\mathbf {v} _{\mathrm {B} }}{c^{2}}}}}}
1284:
1239:
1194:
1148:{\displaystyle \underbrace {\mathbf {v} _{M\mid E}} _{\text{50 km/h}}=\underbrace {\mathbf {v} _{M\mid T}} _{\text{10 km/h}}+\underbrace {\mathbf {v} _{T\mid E}} _{\text{40 km/h}},}
828:
3953:
3385:
2510:
2350:
2166:
860:
2032:
To construct a theory of relative motion consistent with the theory of special relativity, we must adopt a different convention. Continuing to work in the (non-relativistic)
112:
2518:
3937:{\displaystyle \mathbf {v} _{\mathrm {B|A} }={\frac {1}{\gamma _{\mathrm {A} }\left(1-{\frac {\mathbf {v} _{\mathrm {A} }\mathbf {v} _{\mathrm {B} }}{c^{2}}}\right)}}\left}
2081:
2203:
2113:
2458:
1867:
1302:
occurs because this equation for relative velocity falsely predicts that different observers will measure different speeds when observing the motion of light.
2433:
1947:
2744:
1689:
778:
3604:{\displaystyle v_{\mathrm {B|A} }={\frac {\sqrt {c^{4}-\left(c^{2}-v_{\mathrm {A} }^{2}\right)\left(c^{2}-v_{\mathrm {B} }^{2}\right)}}{c}}}
1403:
1332:
367:
3369:{\displaystyle \mathbf {v} _{\mathrm {B|A} }={\frac {\mathbf {v} _{\mathrm {B} }}{\gamma _{\mathrm {A} }}}-\mathbf {v} _{\mathrm {A} }}
486:
459:
4317:
This result is valid if all motion is restricted to the x-axis, but can be easily generalized by replacing the first equation by
4320:
44:
1019:
925:
2211:
865:
2941:{\displaystyle \|\mathbf {v} _{\mathrm {B|A} }\|=\|\mathbf {v} _{\mathrm {A|B} }\|=v_{\mathrm {B|A} }=v_{\mathrm {A|B} }}
1812:
1760:
441:
1482:
4462:
771:
4254:
3622:
3248:
2690:
1299:
4539:
733:
2678:
107:
362:
102:
4024:{\displaystyle \gamma _{\mathrm {A} }={\frac {1}{\sqrt {1-\left({\frac {v_{\mathrm {A} }}{c}}\right)^{2}}}}}
3456:{\displaystyle \gamma _{\mathrm {A} }={\frac {1}{\sqrt {1-\left({\frac {v_{\mathrm {A} }}{c}}\right)^{2}}}}}
3245:
In the case where two objects are traveling in perpendicular directions, the relativistic relative velocity
2819:
rotate the coordinate system. This rotation has no effect on the magnitude of a vector, and hence relative
1254:
1209:
1164:
798:
4625:
4620:
764:
751:
512:
435:
357:
200:
4630:
2468:
is the motion of a stationary object in the primed frame, as seen from the unprimed frame. Thus we have
2355:
431:
232:
210:
4530:
4289:
2659:{\displaystyle v_{A\mid O'}=v_{A\mid O}-v_{O'\mid O}\Rightarrow v_{A\mid O}=v_{A\mid O'}+v_{O'\mid O},}
2302:
833:
651:
540:
466:
326:
259:
2682:
405:
2471:
681:
525:
4380:
is defined in the prime or unprimed reference frame. It might help to visualize the fact that if
2121:
2037:
1012:
631:
395:
1937:{\displaystyle \mathbf {v} _{B\mid A}=\mathbf {v} _{B\mid C}-\mathbf {v} _{A\mid C}\Rightarrow }
671:
2816:
676:
493:
4442:
2046:
686:
661:
347:
165:
2171:
1011:) that all speeds are much less than the speed of light. This limit is associated with the
706:
666:
574:
570:
562:
552:
342:
335:
91:
4421:′ is valid only in the approximation that the speed is much less than that of light.
2734:. However, unlike the case of classical mechanics, in Special Relativity, it is generally
2087:
701:
8:
4604:
4492:
2033:
1023:
1008:
1000:
481:
422:
400:
145:
140:
135:
35:
2438:
4592:
4580:
4284:
2418:
1027:
1004:
611:
352:
227:
195:
155:
4635:
4458:
4259:
2812:
2017:{\displaystyle \mathbf {v} _{B\mid C}=\mathbf {v} _{B\mid A}+\mathbf {v} _{A\mid C}.}
621:
578:
535:
530:
247:
237:
130:
2464:
as seen by an observer in the unprimed and primed frame, respectively. Recall that
4556:
2287:
To recover the previous expressions for relative velocity, we assume that particle
904:
716:
696:
641:
636:
582:
557:
412:
270:
215:
190:
4274:
711:
656:
606:
601:
520:
16:
Velocity of an object or observer in the rest frame of another object or observer
4544:
4497:
4249:
738:
646:
547:
264:
19:
4515:
4502:
4614:
4410:
4264:
626:
453:
4392:′ = 0, meaning that a particle that is following the path
2801:{\displaystyle \mathbf {v} _{\mathrm {B|A} }=-\mathbf {v} _{\mathrm {A|B} }}
2291:
is following the path defined by dx/dt in the unprimed reference (and hence
4568:
4308:
For example, replace the "Man" by a photon traveling at the speed of light.
691:
616:
305:
185:
1747:{\displaystyle \mathbf {v} _{B\mid A}=\mathbf {v} _{B}-\mathbf {v} _{A}.}
983:
4269:
2687:
As in classical mechanics, in special relativity the relative velocity
912:
476:
150:
1479:
equal to zero). The difference between the two displacement vectors,
1461:{\displaystyle \mathbf {r} _{B}=\mathbf {r} _{Bi}+\mathbf {v} _{B}t,}
1390:{\displaystyle \mathbf {r} _{A}=\mathbf {r} _{Ai}+\mathbf {v} _{A}t,}
498:
1310:
4441:
Fock 1964 The theory of Space Time and
Gravitation, retrieved from
4279:
901:
417:
300:
275:
2669:
where the latter form has the desired (easily learned) symmetry.
390:
243:
160:
4482:
KHURMI R.S., Mechanics, Engineering
Mechanics, Statics, Dynamics
1314:
Relative velocities between two particles in classical mechanics
449:
295:
205:
4505:
Relative motion of two train (1)...(3). Videos on the portal
4498:
A Java applet illustrating
Relative Velocity, by Andrew Duffy
2820:
2027:
285:
280:
222:
4518:
Relative tranquility of trout in creek. Video on the portal
4443:
https://archive.org/details/TheTheoryOfSpaceTimeGravitation
1326:
moving at constant velocity. The equations of motion are:
290:
253:
4563:
4357:{\displaystyle \mathbf {r} \,'=\mathbf {r} -\mathbf {v} t}
83:{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}
4519:
4506:
1305:
4372:
It is easy to be confused about the minus sign before
994:
975:{\displaystyle v_{B\mid A}=\|\mathbf {v} _{B\mid A}\|}
4528:
4323:
4043:
3956:
3675:
3625:
3475:
3388:
3293:
3251:
3106:
2965:
2832:
2747:
2693:
2521:
2474:
2441:
2421:
2358:
2305:
2277:{\displaystyle {\frac {dx'}{dt'}}={\frac {dx}{dt}}-v}
2214:
2174:
2124:
2090:
2049:
1950:
1870:
1815:
1763:
1692:
1532:
1485:
1406:
1335:
1257:
1212:
1167:
1039:
928:
893:{\displaystyle \mathbf {v} _{B\operatorname {rel} A}}
868:
836:
801:
47:
2168:, and what may seem like the obvious statement that
1854:{\displaystyle \mathbf {v} _{B|C}=\mathbf {v} _{B}}
1802:{\displaystyle \mathbf {v} _{A|C}=\mathbf {v} _{A}}
4476:McGraw Hill Dictionary of Physics and Mathematics.
4457:Alonso & Finn, Fundamental University Physics
4356:
4255:Non-Euclidean geometry § Kinematic geometries
4232:
4023:
3936:
3650:
3603:
3455:
3368:
3276:
3229:
3082:
2940:
2800:
2718:
2658:
2504:
2452:
2427:
2407:
2344:
2276:
2197:
2160:
2107:
2075:
2016:
1936:
1853:
1801:
1746:
1672:
1515:
1460:
1389:
1278:
1233:
1188:
1147:
974:
892:
854:
822:
82:
1516:{\displaystyle \mathbf {r} _{B}-\mathbf {r} _{A}}
4612:
3662:in the rest frame of another object or observer
2730:in the rest frame of another object or observer
1523:, represents the location of B as seen from A.
3619:The general formula for the relative velocity
2679:Special relativity – Composition of velocities
1030:, we generalize the example into an equation:
3651:{\displaystyle \mathbf {v} _{\mathrm {B|A} }}
3277:{\displaystyle \mathbf {v} _{\mathrm {B|A} }}
2811:This peculiar lack of symmetry is related to
2719:{\displaystyle \mathbf {v} _{\mathrm {B|A} }}
772:
4467:Greenwood, Donald T, Principles of Dynamics.
2889:
2864:
2858:
2833:
1475:refers to the initial displacement (at time
969:
948:
4034:The relative speed is given by the formula
3466:The relative speed is given by the formula
3240:
2028:Galilean transformation (non-relativistic)
779:
765:
4400:is at rest in the primed reference frame.
4330:
2726:is the velocity of an object or observer
2151:
1020:The train-and-platform thought experiment
4473:Beer and Johnston, Statics and Dynamics.
1309:
18:
4613:
2951:
1279:{\displaystyle \mathbf {v} _{T\mid E}}
1234:{\displaystyle \mathbf {v} _{M\mid T}}
1189:{\displaystyle \mathbf {v} _{M\mid E}}
989:
823:{\displaystyle \mathbf {v} _{B\mid A}}
2672:
999:We begin with relative motion in the
461:Newton's law of universal gravitation
2299:′ in the primed frame). Thus
1306:In two dimensions (non-relativistic)
2408:{\displaystyle dx'/dt=v_{A\mid O'}}
995:In one dimension (non-relativistic)
442:Mechanics of planar particle motion
50:
13:
4479:Rindler, W., Essential Relativity.
4451:
4203:
4186:
4142:
4102:
4058:
4050:
3997:
3963:
3905:
3892:
3875:
3844:
3829:
3812:
3795:
3755:
3741:
3713:
3692:
3684:
3642:
3634:
3579:
3539:
3490:
3482:
3429:
3395:
3360:
3341:
3329:
3310:
3302:
3268:
3260:
3205:
3191:
3162:
3145:
3121:
3113:
3058:
3044:
3019:
3002:
2982:
2974:
2932:
2924:
2909:
2901:
2883:
2875:
2852:
2844:
2792:
2784:
2764:
2756:
2710:
2702:
1026:model of relative motion violates
14:
4647:
4486:
2815:and the fact that two successive
2345:{\displaystyle dx/dt=v_{A\mid O}}
855:{\displaystyle \mathbf {v} _{BA}}
4598:
4586:
4574:
4562:
4550:
4538:
4347:
4339:
4325:
4197:
4180:
3886:
3869:
3823:
3806:
3789:
3749:
3735:
3678:
3628:
3354:
3323:
3296:
3254:
3199:
3185:
3156:
3139:
3052:
3038:
3013:
2996:
2968:
2869:
2838:
2778:
2750:
2696:
1995:
1974:
1953:
1915:
1894:
1873:
1841:
1818:
1789:
1766:
1731:
1716:
1695:
1639:
1624:
1587:
1569:
1550:
1535:
1503:
1488:
1442:
1424:
1409:
1371:
1353:
1338:
1260:
1215:
1170:
1115:
1080:
1045:
953:
871:
839:
804:
746:
745:
732:
65:
4493:Relative Motion at HyperPhysics
3614:
1757:After making the substitutions
1300:violation of special relativity
4435:
4403:
4366:
4311:
4302:
4054:
3856:
3835:
3688:
3638:
3486:
3306:
3264:
3117:
2978:
2928:
2905:
2879:
2848:
2788:
2760:
2706:
2586:
2505:{\displaystyle v=v_{O'\mid O}}
1931:
1827:
1775:
1649:
1619:
915:of another object or observer
1:
4470:Goodman and Warner, Dynamics.
4428:
1318:The figure shows two objects
368:Koopman–von Neumann mechanics
2161:{\displaystyle dx'=dx-v\,dt}
436:Non-inertial reference frame
23:Relative motion man on train
7:
4243:
363:Appell's equation of motion
233:Inertial frame of reference
10:
4652:
4409:Keep in mind that, due to
4290:Space velocity (astronomy)
2676:
1022:.) To recognize that this
986:of the relative velocity.
3666:is given by the formula:
3658:of an object or observer
3284:is given by the formula:
3097:is given by the formula:
2683:Velocity-addition formula
907:of an object or observer
4503:RelatĂv mozgás (1)...(3)
4295:
3241:Perpendicular velocities
526:Rotating reference frame
358:Hamilton–Jacobi equation
2817:Lorentz transformations
2076:{\displaystyle x'=x-vt}
2038:Galilean transformation
1286:is the velocity of the
1241:is the velocity of the
1196:is the velocity of the
1013:Galilean transformation
1009:Newtonian approximation
467:Newton's laws of motion
327:Newton's laws of motion
4358:
4234:
4025:
3938:
3652:
3605:
3457:
3370:
3278:
3231:
3084:
2942:
2802:
2720:
2660:
2506:
2454:
2429:
2409:
2346:
2278:
2199:
2198:{\displaystyle dt'=dt}
2162:
2109:
2077:
2018:
1938:
1855:
1803:
1748:
1674:
1517:
1462:
1391:
1315:
1280:
1235:
1190:
1149:
976:
894:
856:
824:
494:Simple harmonic motion
407:Euler's laws of motion
201:D'Alembert's principle
84:
24:
4516:Sebességek összegzése
4359:
4235:
4026:
3939:
3653:
3606:
3458:
3371:
3279:
3232:
3085:
2943:
2803:
2721:
2677:Further information:
2661:
2507:
2455:
2430:
2410:
2347:
2279:
2200:
2163:
2110:
2078:
2019:
1939:
1856:
1804:
1749:
1675:
1518:
1463:
1392:
1313:
1281:
1236:
1191:
1150:
977:
895:
857:
825:
348:Hamiltonian mechanics
166:Statistical mechanics
85:
22:
4321:
4041:
3954:
3673:
3623:
3473:
3386:
3291:
3249:
3104:
2963:
2830:
2745:
2691:
2519:
2472:
2439:
2419:
2356:
2303:
2212:
2172:
2122:
2108:{\displaystyle t'=t}
2088:
2047:
1948:
1868:
1813:
1761:
1690:
1530:
1483:
1471:where the subscript
1404:
1333:
1255:
1210:
1165:
1037:
926:
866:
834:
799:
571:Angular acceleration
563:Rotational frequency
343:Lagrangian mechanics
336:Analytical mechanics
92:Second law of motion
45:
4626:Classical mechanics
4621:Physical quantities
4152:
4112:
3915:
3589:
3549:
2952:Parallel velocities
2460:refer to motion of
1245:an relative to the
990:Classical mechanics
423:Harmonic oscillator
401:Equations of motion
36:Classical mechanics
30:Part of a series on
4631:Special relativity
4354:
4285:Relativistic speed
4230:
4136:
4096:
4021:
3934:
3899:
3648:
3601:
3573:
3533:
3453:
3366:
3274:
3227:
3080:
2938:
2798:
2716:
2673:Special relativity
2656:
2502:
2453:{\displaystyle O'}
2450:
2425:
2405:
2342:
2274:
2195:
2158:
2105:
2073:
2040:in one dimension:
2014:
1934:
1851:
1799:
1744:
1670:
1666:
1659:
1611:
1608:initial separation
1604:
1513:
1458:
1387:
1316:
1276:
1231:
1186:
1145:
1141:
1134:
1106:
1099:
1071:
1064:
1028:special relativity
972:
890:
852:
820:
739:Physics portal
353:Routhian mechanics
228:Frame of reference
80:
25:
4260:Peculiar velocity
4222:
4220:
4019:
4018:
4006:
3916:
3780:
3772:
3599:
3595:
3451:
3450:
3438:
3347:
3225:
3222:
3078:
3075:
2813:Thomas precession
2428:{\displaystyle O}
2266:
2243:
1664:
1663:relative velocity
1617:
1615:
1609:
1565:
1563:
1290:rain relative to
1139:
1112:
1110:
1104:
1077:
1075:
1069:
1042:
1040:
793:relative velocity
789:
788:
536:Centrifugal force
531:Centripetal force
487:Euler's equations
472:Relative velocity
248:Moment of inertia
78:
52:
4643:
4603:
4602:
4601:
4591:
4590:
4589:
4579:
4578:
4577:
4567:
4566:
4555:
4554:
4553:
4543:
4542:
4534:
4525:
4512:
4445:
4439:
4422:
4407:
4401:
4370:
4364:
4363:
4361:
4360:
4355:
4350:
4342:
4334:
4328:
4315:
4309:
4306:
4239:
4237:
4236:
4231:
4223:
4221:
4219:
4218:
4213:
4209:
4208:
4207:
4206:
4200:
4191:
4190:
4189:
4183:
4174:
4173:
4158:
4157:
4153:
4151:
4146:
4145:
4132:
4131:
4117:
4113:
4111:
4106:
4105:
4092:
4091:
4076:
4068:
4063:
4062:
4061:
4057:
4030:
4028:
4027:
4022:
4020:
4017:
4016:
4011:
4007:
4002:
4001:
4000:
3990:
3977:
3973:
3968:
3967:
3966:
3943:
3941:
3940:
3935:
3933:
3929:
3928:
3924:
3917:
3914:
3909:
3908:
3898:
3897:
3896:
3895:
3889:
3880:
3879:
3878:
3872:
3865:
3849:
3848:
3847:
3834:
3833:
3832:
3826:
3817:
3816:
3815:
3809:
3800:
3799:
3798:
3792:
3781:
3779:
3778:
3774:
3773:
3771:
3770:
3761:
3760:
3759:
3758:
3752:
3746:
3745:
3744:
3738:
3731:
3718:
3717:
3716:
3702:
3697:
3696:
3695:
3691:
3681:
3657:
3655:
3654:
3649:
3647:
3646:
3645:
3641:
3631:
3610:
3608:
3607:
3602:
3600:
3594:
3590:
3588:
3583:
3582:
3569:
3568:
3554:
3550:
3548:
3543:
3542:
3529:
3528:
3511:
3510:
3501:
3500:
3495:
3494:
3493:
3489:
3462:
3460:
3459:
3454:
3452:
3449:
3448:
3443:
3439:
3434:
3433:
3432:
3422:
3409:
3405:
3400:
3399:
3398:
3375:
3373:
3372:
3367:
3365:
3364:
3363:
3357:
3348:
3346:
3345:
3344:
3334:
3333:
3332:
3326:
3320:
3315:
3314:
3313:
3309:
3299:
3283:
3281:
3280:
3275:
3273:
3272:
3271:
3267:
3257:
3236:
3234:
3233:
3228:
3226:
3224:
3223:
3221:
3220:
3211:
3210:
3209:
3208:
3202:
3196:
3195:
3194:
3188:
3181:
3172:
3168:
3167:
3166:
3165:
3159:
3150:
3149:
3148:
3142:
3131:
3126:
3125:
3124:
3120:
3089:
3087:
3086:
3081:
3079:
3077:
3076:
3074:
3073:
3064:
3063:
3062:
3061:
3055:
3049:
3048:
3047:
3041:
3034:
3025:
3024:
3023:
3022:
3016:
3007:
3006:
3005:
2999:
2992:
2987:
2986:
2985:
2981:
2971:
2947:
2945:
2944:
2939:
2937:
2936:
2935:
2931:
2914:
2913:
2912:
2908:
2888:
2887:
2886:
2882:
2872:
2857:
2856:
2855:
2851:
2841:
2823:is symmetrical.
2807:
2805:
2804:
2799:
2797:
2796:
2795:
2791:
2781:
2769:
2768:
2767:
2763:
2753:
2725:
2723:
2722:
2717:
2715:
2714:
2713:
2709:
2699:
2665:
2663:
2662:
2657:
2652:
2651:
2644:
2628:
2627:
2626:
2604:
2603:
2585:
2584:
2577:
2561:
2560:
2542:
2541:
2540:
2511:
2509:
2508:
2503:
2501:
2500:
2493:
2459:
2457:
2456:
2451:
2449:
2434:
2432:
2431:
2426:
2414:
2412:
2411:
2406:
2404:
2403:
2402:
2374:
2369:
2351:
2349:
2348:
2343:
2341:
2340:
2316:
2283:
2281:
2280:
2275:
2267:
2265:
2257:
2249:
2244:
2242:
2241:
2229:
2228:
2216:
2204:
2202:
2201:
2196:
2185:
2167:
2165:
2164:
2159:
2135:
2114:
2112:
2111:
2106:
2098:
2082:
2080:
2079:
2074:
2057:
2036:we begin with a
2023:
2021:
2020:
2015:
2010:
2009:
1998:
1989:
1988:
1977:
1968:
1967:
1956:
1943:
1941:
1940:
1935:
1930:
1929:
1918:
1909:
1908:
1897:
1888:
1887:
1876:
1860:
1858:
1857:
1852:
1850:
1849:
1844:
1835:
1834:
1830:
1821:
1808:
1806:
1805:
1800:
1798:
1797:
1792:
1783:
1782:
1778:
1769:
1753:
1751:
1750:
1745:
1740:
1739:
1734:
1725:
1724:
1719:
1710:
1709:
1698:
1679:
1677:
1676:
1671:
1665:
1662:
1660:
1655:
1648:
1647:
1642:
1633:
1632:
1627:
1610:
1607:
1605:
1600:
1599:
1598:
1590:
1581:
1580:
1572:
1559:
1558:
1553:
1544:
1543:
1538:
1522:
1520:
1519:
1514:
1512:
1511:
1506:
1497:
1496:
1491:
1467:
1465:
1464:
1459:
1451:
1450:
1445:
1436:
1435:
1427:
1418:
1417:
1412:
1396:
1394:
1393:
1388:
1380:
1379:
1374:
1365:
1364:
1356:
1347:
1346:
1341:
1285:
1283:
1282:
1277:
1275:
1274:
1263:
1240:
1238:
1237:
1232:
1230:
1229:
1218:
1195:
1193:
1192:
1187:
1185:
1184:
1173:
1154:
1152:
1151:
1146:
1140:
1137:
1135:
1130:
1129:
1118:
1105:
1102:
1100:
1095:
1094:
1083:
1070:
1067:
1065:
1060:
1059:
1048:
981:
979:
978:
973:
968:
967:
956:
944:
943:
899:
897:
896:
891:
889:
888:
874:
861:
859:
858:
853:
851:
850:
842:
829:
827:
826:
821:
819:
818:
807:
781:
774:
767:
754:
749:
748:
741:
737:
736:
642:Johann Bernoulli
637:Daniel Bernoulli
558:Tangential speed
462:
438:
413:Fictitious force
408:
260:Mechanical power
250:
191:Angular momentum
89:
87:
86:
81:
79:
77:
69:
68:
59:
54:
53:
27:
26:
4651:
4650:
4646:
4645:
4644:
4642:
4641:
4640:
4611:
4610:
4609:
4599:
4597:
4587:
4585:
4575:
4573:
4561:
4551:
4549:
4537:
4529:
4523:
4510:
4489:
4454:
4452:Further reading
4449:
4448:
4440:
4436:
4431:
4426:
4425:
4408:
4404:
4371:
4367:
4346:
4338:
4329:
4324:
4322:
4319:
4318:
4316:
4312:
4307:
4303:
4298:
4275:Radial velocity
4246:
4214:
4202:
4201:
4196:
4195:
4185:
4184:
4179:
4178:
4169:
4165:
4164:
4160:
4159:
4147:
4141:
4140:
4127:
4123:
4122:
4118:
4107:
4101:
4100:
4087:
4083:
4082:
4078:
4077:
4075:
4067:
4053:
4049:
4048:
4044:
4042:
4039:
4038:
4012:
3996:
3995:
3991:
3989:
3985:
3984:
3972:
3962:
3961:
3957:
3955:
3952:
3951:
3910:
3904:
3903:
3891:
3890:
3885:
3884:
3874:
3873:
3868:
3867:
3866:
3864:
3863:
3859:
3843:
3842:
3838:
3828:
3827:
3822:
3821:
3811:
3810:
3805:
3804:
3794:
3793:
3788:
3787:
3786:
3782:
3766:
3762:
3754:
3753:
3748:
3747:
3740:
3739:
3734:
3733:
3732:
3730:
3723:
3719:
3712:
3711:
3707:
3706:
3701:
3687:
3683:
3682:
3677:
3676:
3674:
3671:
3670:
3637:
3633:
3632:
3627:
3626:
3624:
3621:
3620:
3617:
3584:
3578:
3577:
3564:
3560:
3559:
3555:
3544:
3538:
3537:
3524:
3520:
3519:
3515:
3506:
3502:
3499:
3485:
3481:
3480:
3476:
3474:
3471:
3470:
3444:
3428:
3427:
3423:
3421:
3417:
3416:
3404:
3394:
3393:
3389:
3387:
3384:
3383:
3359:
3358:
3353:
3352:
3340:
3339:
3335:
3328:
3327:
3322:
3321:
3319:
3305:
3301:
3300:
3295:
3294:
3292:
3289:
3288:
3263:
3259:
3258:
3253:
3252:
3250:
3247:
3246:
3243:
3216:
3212:
3204:
3203:
3198:
3197:
3190:
3189:
3184:
3183:
3182:
3180:
3173:
3161:
3160:
3155:
3154:
3144:
3143:
3138:
3137:
3136:
3132:
3130:
3116:
3112:
3111:
3107:
3105:
3102:
3101:
3069:
3065:
3057:
3056:
3051:
3050:
3043:
3042:
3037:
3036:
3035:
3033:
3026:
3018:
3017:
3012:
3011:
3001:
3000:
2995:
2994:
2993:
2991:
2977:
2973:
2972:
2967:
2966:
2964:
2961:
2960:
2954:
2927:
2923:
2922:
2918:
2904:
2900:
2899:
2895:
2878:
2874:
2873:
2868:
2867:
2847:
2843:
2842:
2837:
2836:
2831:
2828:
2827:
2787:
2783:
2782:
2777:
2776:
2759:
2755:
2754:
2749:
2748:
2746:
2743:
2742:
2705:
2701:
2700:
2695:
2694:
2692:
2689:
2688:
2685:
2675:
2637:
2636:
2632:
2619:
2612:
2608:
2593:
2589:
2570:
2569:
2565:
2550:
2546:
2533:
2526:
2522:
2520:
2517:
2516:
2486:
2485:
2481:
2473:
2470:
2469:
2442:
2440:
2437:
2436:
2420:
2417:
2416:
2395:
2388:
2384:
2370:
2362:
2357:
2354:
2353:
2330:
2326:
2312:
2304:
2301:
2300:
2258:
2250:
2248:
2234:
2230:
2221:
2217:
2215:
2213:
2210:
2209:
2178:
2173:
2170:
2169:
2128:
2123:
2120:
2119:
2091:
2089:
2086:
2085:
2050:
2048:
2045:
2044:
2034:Newtonian limit
2030:
1999:
1994:
1993:
1978:
1973:
1972:
1957:
1952:
1951:
1949:
1946:
1945:
1919:
1914:
1913:
1898:
1893:
1892:
1877:
1872:
1871:
1869:
1866:
1865:
1845:
1840:
1839:
1826:
1822:
1817:
1816:
1814:
1811:
1810:
1793:
1788:
1787:
1774:
1770:
1765:
1764:
1762:
1759:
1758:
1735:
1730:
1729:
1720:
1715:
1714:
1699:
1694:
1693:
1691:
1688:
1687:
1661:
1643:
1638:
1637:
1628:
1623:
1622:
1618:
1616:
1606:
1591:
1586:
1585:
1573:
1568:
1567:
1566:
1564:
1554:
1549:
1548:
1539:
1534:
1533:
1531:
1528:
1527:
1507:
1502:
1501:
1492:
1487:
1486:
1484:
1481:
1480:
1446:
1441:
1440:
1428:
1423:
1422:
1413:
1408:
1407:
1405:
1402:
1401:
1375:
1370:
1369:
1357:
1352:
1351:
1342:
1337:
1336:
1334:
1331:
1330:
1308:
1264:
1259:
1258:
1256:
1253:
1252:
1219:
1214:
1213:
1211:
1208:
1207:
1200:an relative to
1174:
1169:
1168:
1166:
1163:
1162:
1136:
1119:
1114:
1113:
1111:
1101:
1084:
1079:
1078:
1076:
1066:
1049:
1044:
1043:
1041:
1038:
1035:
1034:
997:
992:
957:
952:
951:
933:
929:
927:
924:
923:
875:
870:
869:
867:
864:
863:
843:
838:
837:
835:
832:
831:
808:
803:
802:
800:
797:
796:
785:
744:
731:
730:
723:
722:
721:
596:
588:
587:
567:
521:Circular motion
515:
505:
504:
503:
460:
430:
427:
406:
385:
377:
376:
373:
372:
330:
320:
312:
311:
310:
269:
265:Mechanical work
258:
242:
180:
172:
171:
170:
125:
117:
94:
70:
64:
60:
58:
49:
48:
46:
43:
42:
17:
12:
11:
5:
4649:
4639:
4638:
4633:
4628:
4623:
4608:
4607:
4595:
4583:
4571:
4559:
4547:
4527:
4526:
4524:(in Hungarian)
4513:
4511:(in Hungarian)
4500:
4495:
4488:
4487:External links
4485:
4484:
4483:
4480:
4477:
4474:
4471:
4468:
4465:
4453:
4450:
4447:
4446:
4433:
4432:
4430:
4427:
4424:
4423:
4402:
4365:
4353:
4349:
4345:
4341:
4337:
4333:
4327:
4310:
4300:
4299:
4297:
4294:
4293:
4292:
4287:
4282:
4277:
4272:
4267:
4262:
4257:
4252:
4250:Doppler effect
4245:
4242:
4241:
4240:
4229:
4226:
4217:
4212:
4205:
4199:
4194:
4188:
4182:
4177:
4172:
4168:
4163:
4156:
4150:
4144:
4139:
4135:
4130:
4126:
4121:
4116:
4110:
4104:
4099:
4095:
4090:
4086:
4081:
4074:
4071:
4066:
4060:
4056:
4052:
4047:
4032:
4031:
4015:
4010:
4005:
3999:
3994:
3988:
3983:
3980:
3976:
3971:
3965:
3960:
3945:
3944:
3932:
3927:
3923:
3920:
3913:
3907:
3902:
3894:
3888:
3883:
3877:
3871:
3862:
3858:
3855:
3852:
3846:
3841:
3837:
3831:
3825:
3820:
3814:
3808:
3803:
3797:
3791:
3785:
3777:
3769:
3765:
3757:
3751:
3743:
3737:
3729:
3726:
3722:
3715:
3710:
3705:
3700:
3694:
3690:
3686:
3680:
3644:
3640:
3636:
3630:
3616:
3613:
3612:
3611:
3598:
3593:
3587:
3581:
3576:
3572:
3567:
3563:
3558:
3553:
3547:
3541:
3536:
3532:
3527:
3523:
3518:
3514:
3509:
3505:
3498:
3492:
3488:
3484:
3479:
3464:
3463:
3447:
3442:
3437:
3431:
3426:
3420:
3415:
3412:
3408:
3403:
3397:
3392:
3377:
3376:
3362:
3356:
3351:
3343:
3338:
3331:
3325:
3318:
3312:
3308:
3304:
3298:
3270:
3266:
3262:
3256:
3242:
3239:
3238:
3237:
3219:
3215:
3207:
3201:
3193:
3187:
3179:
3176:
3171:
3164:
3158:
3153:
3147:
3141:
3135:
3129:
3123:
3119:
3115:
3110:
3095:relative speed
3091:
3090:
3072:
3068:
3060:
3054:
3046:
3040:
3032:
3029:
3021:
3015:
3010:
3004:
2998:
2990:
2984:
2980:
2976:
2970:
2953:
2950:
2949:
2948:
2934:
2930:
2926:
2921:
2917:
2911:
2907:
2903:
2898:
2894:
2891:
2885:
2881:
2877:
2871:
2866:
2863:
2860:
2854:
2850:
2846:
2840:
2835:
2809:
2808:
2794:
2790:
2786:
2780:
2775:
2772:
2766:
2762:
2758:
2752:
2738:the case that
2712:
2708:
2704:
2698:
2674:
2671:
2667:
2666:
2655:
2650:
2647:
2643:
2640:
2635:
2631:
2625:
2622:
2618:
2615:
2611:
2607:
2602:
2599:
2596:
2592:
2588:
2583:
2580:
2576:
2573:
2568:
2564:
2559:
2556:
2553:
2549:
2545:
2539:
2536:
2532:
2529:
2525:
2499:
2496:
2492:
2489:
2484:
2480:
2477:
2448:
2445:
2424:
2401:
2398:
2394:
2391:
2387:
2383:
2380:
2377:
2373:
2368:
2365:
2361:
2339:
2336:
2333:
2329:
2325:
2322:
2319:
2315:
2311:
2308:
2285:
2284:
2273:
2270:
2264:
2261:
2256:
2253:
2247:
2240:
2237:
2233:
2227:
2224:
2220:
2194:
2191:
2188:
2184:
2181:
2177:
2157:
2154:
2150:
2147:
2144:
2141:
2138:
2134:
2131:
2127:
2116:
2115:
2104:
2101:
2097:
2094:
2083:
2072:
2069:
2066:
2063:
2060:
2056:
2053:
2029:
2026:
2025:
2024:
2013:
2008:
2005:
2002:
1997:
1992:
1987:
1984:
1981:
1976:
1971:
1966:
1963:
1960:
1955:
1933:
1928:
1925:
1922:
1917:
1912:
1907:
1904:
1901:
1896:
1891:
1886:
1883:
1880:
1875:
1848:
1843:
1838:
1833:
1829:
1825:
1820:
1796:
1791:
1786:
1781:
1777:
1773:
1768:
1755:
1754:
1743:
1738:
1733:
1728:
1723:
1718:
1713:
1708:
1705:
1702:
1697:
1681:
1680:
1669:
1658:
1654:
1651:
1646:
1641:
1636:
1631:
1626:
1621:
1614:
1603:
1597:
1594:
1589:
1584:
1579:
1576:
1571:
1562:
1557:
1552:
1547:
1542:
1537:
1510:
1505:
1500:
1495:
1490:
1469:
1468:
1457:
1454:
1449:
1444:
1439:
1434:
1431:
1426:
1421:
1416:
1411:
1398:
1397:
1386:
1383:
1378:
1373:
1368:
1363:
1360:
1355:
1350:
1345:
1340:
1307:
1304:
1296:
1295:
1273:
1270:
1267:
1262:
1250:
1228:
1225:
1222:
1217:
1205:
1183:
1180:
1177:
1172:
1156:
1155:
1144:
1133:
1128:
1125:
1122:
1117:
1109:
1098:
1093:
1090:
1087:
1082:
1074:
1063:
1058:
1055:
1052:
1047:
996:
993:
991:
988:
971:
966:
963:
960:
955:
950:
947:
942:
939:
936:
932:
921:relative speed
887:
884:
881:
878:
873:
849:
846:
841:
817:
814:
811:
806:
787:
786:
784:
783:
776:
769:
761:
758:
757:
756:
755:
742:
725:
724:
720:
719:
714:
709:
704:
699:
694:
689:
684:
679:
674:
669:
664:
659:
654:
649:
644:
639:
634:
629:
624:
619:
614:
609:
604:
598:
597:
594:
593:
590:
589:
586:
585:
566:
565:
560:
555:
550:
548:Coriolis force
545:
544:
543:
533:
528:
523:
517:
516:
511:
510:
507:
506:
502:
501:
496:
491:
490:
489:
484:
474:
469:
464:
457:
446:
445:
444:
439:
426:
425:
420:
415:
410:
403:
398:
393:
387:
386:
383:
382:
379:
378:
375:
374:
371:
370:
365:
360:
355:
350:
345:
339:
333:
331:
324:
321:
318:
317:
314:
313:
309:
308:
303:
298:
293:
288:
283:
278:
273:
267:
262:
256:
251:
240:
235:
230:
225:
220:
219:
218:
213:
203:
198:
193:
188:
182:
181:
178:
177:
174:
173:
169:
168:
163:
158:
153:
148:
143:
138:
133:
127:
126:
123:
122:
119:
118:
116:
115:
110:
105:
99:
96:
95:
90:
76:
73:
67:
63:
57:
39:
38:
32:
31:
15:
9:
6:
4:
3:
2:
4648:
4637:
4634:
4632:
4629:
4627:
4624:
4622:
4619:
4618:
4616:
4606:
4596:
4594:
4584:
4582:
4572:
4570:
4565:
4560:
4558:
4548:
4546:
4541:
4536:
4535:
4532:
4521:
4517:
4514:
4508:
4504:
4501:
4499:
4496:
4494:
4491:
4490:
4481:
4478:
4475:
4472:
4469:
4466:
4464:
4463:0-201-56518-8
4460:
4456:
4455:
4444:
4438:
4434:
4420:
4417: =
4416:
4412:
4411:time dilation
4406:
4399:
4396: =
4395:
4391:
4387:
4384: =
4383:
4379:
4376:, or whether
4375:
4369:
4351:
4343:
4335:
4331:
4314:
4305:
4301:
4291:
4288:
4286:
4283:
4281:
4278:
4276:
4273:
4271:
4268:
4266:
4265:Proper motion
4263:
4261:
4258:
4256:
4253:
4251:
4248:
4247:
4227:
4224:
4215:
4210:
4192:
4175:
4170:
4166:
4161:
4154:
4148:
4137:
4133:
4128:
4124:
4119:
4114:
4108:
4097:
4093:
4088:
4084:
4079:
4072:
4069:
4064:
4045:
4037:
4036:
4035:
4013:
4008:
4003:
3992:
3986:
3981:
3978:
3974:
3969:
3958:
3950:
3949:
3948:
3930:
3925:
3921:
3918:
3911:
3900:
3881:
3860:
3853:
3850:
3839:
3818:
3801:
3783:
3775:
3767:
3763:
3727:
3724:
3720:
3708:
3703:
3698:
3669:
3668:
3667:
3665:
3661:
3596:
3591:
3585:
3574:
3570:
3565:
3561:
3556:
3551:
3545:
3534:
3530:
3525:
3521:
3516:
3512:
3507:
3503:
3496:
3477:
3469:
3468:
3467:
3445:
3440:
3435:
3424:
3418:
3413:
3410:
3406:
3401:
3390:
3382:
3381:
3380:
3349:
3336:
3316:
3287:
3286:
3285:
3217:
3213:
3177:
3174:
3169:
3151:
3133:
3127:
3108:
3100:
3099:
3098:
3096:
3070:
3066:
3030:
3027:
3008:
2988:
2959:
2958:
2957:
2919:
2915:
2896:
2892:
2861:
2826:
2825:
2824:
2822:
2818:
2814:
2773:
2770:
2741:
2740:
2739:
2737:
2733:
2729:
2684:
2680:
2670:
2653:
2648:
2645:
2641:
2638:
2633:
2629:
2623:
2620:
2616:
2613:
2609:
2605:
2600:
2597:
2594:
2590:
2581:
2578:
2574:
2571:
2566:
2562:
2557:
2554:
2551:
2547:
2543:
2537:
2534:
2530:
2527:
2523:
2515:
2514:
2513:
2497:
2494:
2490:
2487:
2482:
2478:
2475:
2467:
2463:
2446:
2443:
2422:
2399:
2396:
2392:
2389:
2385:
2381:
2378:
2375:
2371:
2366:
2363:
2359:
2337:
2334:
2331:
2327:
2323:
2320:
2317:
2313:
2309:
2306:
2298:
2294:
2290:
2271:
2268:
2262:
2259:
2254:
2251:
2245:
2238:
2235:
2231:
2225:
2222:
2218:
2208:
2207:
2206:
2192:
2189:
2186:
2182:
2179:
2175:
2155:
2152:
2148:
2145:
2142:
2139:
2136:
2132:
2129:
2125:
2102:
2099:
2095:
2092:
2084:
2070:
2067:
2064:
2061:
2058:
2054:
2051:
2043:
2042:
2041:
2039:
2035:
2011:
2006:
2003:
2000:
1990:
1985:
1982:
1979:
1969:
1964:
1961:
1958:
1926:
1923:
1920:
1910:
1905:
1902:
1899:
1889:
1884:
1881:
1878:
1864:
1863:
1862:
1846:
1836:
1831:
1823:
1794:
1784:
1779:
1771:
1741:
1736:
1726:
1721:
1711:
1706:
1703:
1700:
1686:
1685:
1684:
1667:
1656:
1652:
1644:
1634:
1629:
1612:
1601:
1595:
1592:
1582:
1577:
1574:
1560:
1555:
1545:
1540:
1526:
1525:
1524:
1508:
1498:
1493:
1478:
1474:
1455:
1452:
1447:
1437:
1432:
1429:
1419:
1414:
1400:
1399:
1384:
1381:
1376:
1366:
1361:
1358:
1348:
1343:
1329:
1328:
1327:
1325:
1321:
1312:
1303:
1301:
1293:
1289:
1271:
1268:
1265:
1251:
1248:
1244:
1226:
1223:
1220:
1206:
1203:
1199:
1181:
1178:
1175:
1161:
1160:
1159:
1142:
1131:
1126:
1123:
1120:
1107:
1096:
1091:
1088:
1085:
1072:
1061:
1056:
1053:
1050:
1033:
1032:
1031:
1029:
1025:
1021:
1016:
1014:
1010:
1006:
1002:
987:
985:
964:
961:
958:
945:
940:
937:
934:
930:
922:
918:
914:
910:
906:
903:
885:
882:
879:
876:
847:
844:
815:
812:
809:
794:
782:
777:
775:
770:
768:
763:
762:
760:
759:
753:
743:
740:
735:
729:
728:
727:
726:
718:
715:
713:
710:
708:
705:
703:
700:
698:
695:
693:
690:
688:
685:
683:
680:
678:
675:
673:
670:
668:
665:
663:
660:
658:
655:
653:
650:
648:
645:
643:
640:
638:
635:
633:
630:
628:
625:
623:
620:
618:
615:
613:
610:
608:
605:
603:
600:
599:
592:
591:
584:
580:
576:
572:
569:
568:
564:
561:
559:
556:
554:
551:
549:
546:
542:
539:
538:
537:
534:
532:
529:
527:
524:
522:
519:
518:
514:
509:
508:
500:
497:
495:
492:
488:
485:
483:
480:
479:
478:
475:
473:
470:
468:
465:
463:
458:
455:
451:
448:
447:
443:
440:
437:
433:
429:
428:
424:
421:
419:
416:
414:
411:
409:
404:
402:
399:
397:
394:
392:
389:
388:
381:
380:
369:
366:
364:
361:
359:
356:
354:
351:
349:
346:
344:
341:
340:
338:
337:
332:
329:
328:
323:
322:
316:
315:
307:
304:
302:
299:
297:
294:
292:
289:
287:
284:
282:
279:
277:
274:
272:
268:
266:
263:
261:
257:
255:
252:
249:
245:
241:
239:
236:
234:
231:
229:
226:
224:
221:
217:
214:
212:
209:
208:
207:
204:
202:
199:
197:
194:
192:
189:
187:
184:
183:
176:
175:
167:
164:
162:
159:
157:
154:
152:
149:
147:
144:
142:
139:
137:
134:
132:
129:
128:
121:
120:
114:
111:
109:
106:
104:
101:
100:
98:
97:
93:
74:
71:
61:
55:
41:
40:
37:
34:
33:
29:
28:
21:
4605:Solar System
4437:
4418:
4414:
4405:
4397:
4393:
4389:
4385:
4381:
4377:
4373:
4368:
4313:
4304:
4033:
3946:
3663:
3659:
3618:
3615:General case
3465:
3378:
3244:
3094:
3092:
2955:
2810:
2735:
2731:
2727:
2686:
2668:
2465:
2461:
2296:
2292:
2288:
2286:
2117:
2031:
1756:
1682:
1476:
1472:
1470:
1323:
1319:
1317:
1297:
1291:
1287:
1246:
1242:
1201:
1197:
1157:
1017:
1005:relativistic
998:
920:
916:
908:
792:
790:
581: /
577: /
575:displacement
573: /
471:
434: /
396:Displacement
334:
325:
319:Formulations
306:Virtual work
246: /
186:Acceleration
179:Fundamentals
4593:Outer space
4581:Spaceflight
2205:, we have:
1861:, we have:
984:vector norm
717:von Neumann
384:Core topics
4615:Categories
4429:References
4270:Range rate
1007:, or the
1003:, (or non-
913:rest frame
900:), is the
795:, denoted
652:d'Alembert
632:Maupertuis
595:Scientists
477:Rigid body
151:Kinematics
4557:Astronomy
4344:−
4225:⋅
4193:⋅
4176:−
4134:−
4094:−
4073:−
3982:−
3959:γ
3919:−
3882:⋅
3851:−
3840:γ
3802:−
3728:−
3709:γ
3571:−
3531:−
3513:−
3414:−
3391:γ
3350:−
3337:γ
3178:−
3152:−
3031:−
3009:−
2890:‖
2865:‖
2859:‖
2834:‖
2774:−
2646:∣
2617:∣
2598:∣
2587:⇒
2579:∣
2563:−
2555:∣
2531:∣
2495:∣
2393:∣
2335:∣
2269:−
2146:−
2065:−
2004:∣
1983:∣
1962:∣
1932:⇒
1924:∣
1911:−
1903:∣
1882:∣
1727:−
1704:∣
1657:⏟
1635:−
1602:⏟
1583:−
1546:−
1499:−
1269:∣
1224:∣
1179:∣
1132:⏟
1124:∣
1097:⏟
1089:∣
1062:⏟
1054:∣
1024:classical
1001:classical
970:‖
962:∣
949:‖
938:∣
883:
813:∣
697:Liouville
579:frequency
499:Vibration
216:potential
141:Continuum
136:Celestial
113:Textbooks
4636:Velocity
4332:′
4280:Rapidity
4244:See also
2642:′
2624:′
2575:′
2538:′
2491:′
2447:′
2415:, where
2400:′
2367:′
2295:′/
2239:′
2226:′
2183:′
2133:′
2096:′
2055:′
902:velocity
752:Category
677:Hamilton
662:Lagrange
657:Clairaut
622:Horrocks
583:velocity
553:Pendulum
541:reactive
513:Rotation
482:dynamics
432:Inertial
418:Friction
301:Velocity
276:Momentum
156:Kinetics
146:Dynamics
124:Branches
108:Timeline
4545:Physics
4531:Portals
4520:FizKapu
4507:FizKapu
4388:, then
2512:, and:
1944:
1683:Hence:
1158:where:
1138:40 km/h
1103:10 km/h
1068:50 km/h
982:is the
911:in the
712:Koopman
672:Poisson
667:Laplace
612:Huygens
607:Galileo
452: (
391:Damping
244:Inertia
238:Impulse
211:kinetic
161:Statics
131:Applied
103:History
4461:
3947:where
3379:where
919:. The
905:vector
830:(also
750:
702:Appell
687:Cauchy
682:Jacobi
627:Halley
617:Newton
602:Kepler
454:linear
450:Motion
296:Torque
271:Moment
206:Energy
196:Couple
4569:Stars
4296:Notes
2821:speed
1294:arth.
1249:rain,
1204:arth,
707:Gibbs
692:Routh
647:Euler
286:Speed
281:Space
223:Force
4459:ISBN
3093:The
2681:and
2435:and
2352:and
1809:and
1322:and
791:The
291:Time
254:Mass
2736:not
880:rel
862:or
4617::
4522:.
4509:.
4419:dt
4415:dt
4413:,
4398:vt
4386:vt
2297:dt
2293:dx
4533::
4394:x
4390:x
4382:x
4378:v
4374:v
4352:t
4348:v
4340:r
4336:=
4326:r
4228:c
4216:2
4211:)
4204:B
4198:v
4187:A
4181:v
4171:2
4167:c
4162:(
4155:)
4149:2
4143:B
4138:v
4129:2
4125:c
4120:(
4115:)
4109:2
4103:A
4098:v
4089:2
4085:c
4080:(
4070:1
4065:=
4059:A
4055:|
4051:B
4046:v
4014:2
4009:)
4004:c
3998:A
3993:v
3987:(
3979:1
3975:1
3970:=
3964:A
3931:]
3926:)
3922:1
3912:2
3906:A
3901:v
3893:B
3887:v
3876:A
3870:v
3861:(
3857:)
3854:1
3845:A
3836:(
3830:A
3824:v
3819:+
3813:A
3807:v
3796:B
3790:v
3784:[
3776:)
3768:2
3764:c
3756:B
3750:v
3742:A
3736:v
3725:1
3721:(
3714:A
3704:1
3699:=
3693:A
3689:|
3685:B
3679:v
3664:A
3660:B
3643:A
3639:|
3635:B
3629:v
3597:c
3592:)
3586:2
3580:B
3575:v
3566:2
3562:c
3557:(
3552:)
3546:2
3540:A
3535:v
3526:2
3522:c
3517:(
3508:4
3504:c
3497:=
3491:A
3487:|
3483:B
3478:v
3446:2
3441:)
3436:c
3430:A
3425:v
3419:(
3411:1
3407:1
3402:=
3396:A
3361:A
3355:v
3342:A
3330:B
3324:v
3317:=
3311:A
3307:|
3303:B
3297:v
3269:A
3265:|
3261:B
3255:v
3218:2
3214:c
3206:B
3200:v
3192:A
3186:v
3175:1
3170:|
3163:A
3157:v
3146:B
3140:v
3134:|
3128:=
3122:A
3118:|
3114:B
3109:v
3071:2
3067:c
3059:B
3053:v
3045:A
3039:v
3028:1
3020:A
3014:v
3003:B
2997:v
2989:=
2983:A
2979:|
2975:B
2969:v
2933:B
2929:|
2925:A
2920:v
2916:=
2910:A
2906:|
2902:B
2897:v
2893:=
2884:B
2880:|
2876:A
2870:v
2862:=
2853:A
2849:|
2845:B
2839:v
2793:B
2789:|
2785:A
2779:v
2771:=
2765:A
2761:|
2757:B
2751:v
2732:A
2728:B
2711:A
2707:|
2703:B
2697:v
2654:,
2649:O
2639:O
2634:v
2630:+
2621:O
2614:A
2610:v
2606:=
2601:O
2595:A
2591:v
2582:O
2572:O
2567:v
2558:O
2552:A
2548:v
2544:=
2535:O
2528:A
2524:v
2498:O
2488:O
2483:v
2479:=
2476:v
2466:v
2462:A
2444:O
2423:O
2397:O
2390:A
2386:v
2382:=
2379:t
2376:d
2372:/
2364:x
2360:d
2338:O
2332:A
2328:v
2324:=
2321:t
2318:d
2314:/
2310:x
2307:d
2289:A
2272:v
2263:t
2260:d
2255:x
2252:d
2246:=
2236:t
2232:d
2223:x
2219:d
2193:t
2190:d
2187:=
2180:t
2176:d
2156:t
2153:d
2149:v
2143:x
2140:d
2137:=
2130:x
2126:d
2103:t
2100:=
2093:t
2071:t
2068:v
2062:x
2059:=
2052:x
2012:.
2007:C
2001:A
1996:v
1991:+
1986:A
1980:B
1975:v
1970:=
1965:C
1959:B
1954:v
1927:C
1921:A
1916:v
1906:C
1900:B
1895:v
1890:=
1885:A
1879:B
1874:v
1847:B
1842:v
1837:=
1832:C
1828:|
1824:B
1819:v
1795:A
1790:v
1785:=
1780:C
1776:|
1772:A
1767:v
1742:.
1737:A
1732:v
1722:B
1717:v
1712:=
1707:A
1701:B
1696:v
1668:.
1653:t
1650:)
1645:A
1640:v
1630:B
1625:v
1620:(
1613:+
1596:i
1593:A
1588:r
1578:i
1575:B
1570:r
1561:=
1556:A
1551:r
1541:B
1536:r
1509:A
1504:r
1494:B
1489:r
1477:t
1473:i
1456:,
1453:t
1448:B
1443:v
1438:+
1433:i
1430:B
1425:r
1420:=
1415:B
1410:r
1385:,
1382:t
1377:A
1372:v
1367:+
1362:i
1359:A
1354:r
1349:=
1344:A
1339:r
1324:B
1320:A
1292:E
1288:T
1272:E
1266:T
1261:v
1247:T
1243:M
1227:T
1221:M
1216:v
1202:E
1198:M
1182:E
1176:M
1171:v
1143:,
1127:E
1121:T
1116:v
1108:+
1092:T
1086:M
1081:v
1073:=
1057:E
1051:M
1046:v
965:A
959:B
954:v
946:=
941:A
935:B
931:v
917:A
909:B
886:A
877:B
872:v
848:A
845:B
840:v
816:A
810:B
805:v
780:e
773:t
766:v
456:)
75:t
72:d
66:p
62:d
56:=
51:F
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
