Equations of motion | Wikipedia audio article
Channel: wikipedia tts
Date: 25/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Equations_of_motion


00:02:20 1 History
00:04:19 2 Kinematic equations for one particle
00:11:42 2.1 Kinematic quantities
00:11:53 2.2 Uniform acceleration
00:12:04 2.2.1 Constant translational acceleration in a straight line
00:13:39 2.2.2 Constant linear acceleration in any direction
00:15:18 2.2.3 Applications
00:15:42 2.2.4 Constant circular acceleration
00:19:31 2.3 General planar motion
00:19:43 2.4 General 3D motion
00:19:55 3 Dynamic equations of motion
00:20:06 3.1 Newtonian mechanics
00:20:09 3.2 Applications
00:25:29 4 Analytical mechanics
00:27:02 5 Electrodynamics
00:29:17 6 General relativity
00:32:36 6.1 Geodesic equation of motion
00:36:58 6.2 Spinning objects
00:37:08 7 Analogues for waves and fields
00:37:26 7.1 Field equations
00:42:52 7.2 Wave equations
00:47:56 7.3 Quantum theory
00:48:05 8 See also
00:48:15 9 References
00:54:06 Electrodynamics
00:58:03 General relativity
00:58:13 Geodesic equation of motion
01:01:40 x2α − x1α is the separation vector between two geodesics, D/ds (not just d/ds) is the covariant derivative, and Rαβγδ is the Riemann curvature tensor, containing the Christoffel symbols. In other words, the geodesic deviation equation is the equation of motion for masses in curved spacetime, analogous to the Lorentz force equation for charges in an electromagnetic field.For flat spacetime, the metric is a constant tensor so the Christoffel symbols vanish, and the geodesic equation has the solutions of straight lines. This is also the limiting case when masses move according to Newton's law of gravity.
01:02:21 Spinning objects
01:02:30 In general relativity, rotational motion is described by the relativistic angular momentum tensor, including the spin tensor, which enter the equations of motion under covariant derivatives with respect to proper time. The Mathisson–Papapetrou–Dixon equations describe the motion of spinning objects moving in a gravitational field.
01:02:53 Analogues for waves and fields
01:03:35 Field equations
01:04:27 Wave equations
01:06:09 Quantum theory



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SUMMARY
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In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behaviour of a physical system as a set of mathematical functions in terms of dynamic variables: normally spatial coordinates and time are used, but others are also possible, such as momentum components and time. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system. The functions are defined in a Euclidean space in classical mechanics, but are replaced by curved spaces in relativity. If the dynamics of a system is known, the equations are the solutions to the differential equations describing the motion of the dynamics.
There are two main descriptions of motion: dynamics and kinematics. Dynamics is general, since momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
However, kinematics is simpler as it concerns only variables derived from the positions of objects, and time. In circumstances of constant acceleration, these simpler equations of motion are usually referred to as the SUVAT equations, arising from the definitions of kinematic quantities: displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t).
Equations of motion can therefore be grouped under these main classifiers of motion. In all cases, the main types of motion are translations, rotations, oscillations, or any combinations of these.
A differential  ...