Editing Equations of motion (section)

{{short description|Equations that describe the behavior of a physical system}}
[[File:Velocity vs time graph for average acceleration that shows dependence on time.jpg|thumb|360px|<math>v</math> vs <math>t</math> graph for a moving particle under a non-uniform acceleration <math>a</math>.]]
{{Classical mechanics}}

In [[physics]], '''equations of motion''' are [[equation]]s that describe the behavior of a [[physical system]] in terms of its [[Motion (physics)|motion]] as a [[function (mathematics)|function]] of time.<ref name="Physics 1991">{{Cite book | url = https://www.worldcat.org/oclc/20853637 | title = Encyclopedia of Physics | date = 1991 | publisher = VCH Publishers | author1 = R.G. Lerner | author1-link = Rita G. Lerner | author2 = George L. Trigg | isbn = 0-89573-752-3 | edition = second | location = New York | oclc = 20853637}}</ref> More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include [[momentum]] components. The most general choice are [[generalized coordinates]] which can be any convenient variables characteristic of the physical system.<ref name="Analytical Mechanics 2008">{{cite book | last = Hand | first = Louis N. | author2 = Janet D. Finch | url = https://www.worldcat.org/oclc/37903527 | title = Analytical Mechanics | date = 1998 | publisher = Cambridge University Press | isbn = 978-0-521-57572-0 | location = Cambridge | oclc = 37903527}}</ref> The functions are defined in a [[Euclidean space]] in [[classical mechanics]], but are replaced by [[curved space]]s in [[Theory of relativity|relativity]]. If the [[Dynamics (mechanics)|dynamics]] of a system is known, the equations are the solutions for the [[differential equations]] describing the motion of the dynamics.