Lagrangian

A Lagrangian mathcal{L} of a dynamical system, named after Joseph Louis Lagrange, is a functional of the dynamical variables arphi_i(s) which concisely describes the equations of motion of the system. The equations of motion are obtained by means of an action principle, written as

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: rac{delta mathcal{S}}{delta arphi_i} = 0

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where the action mathcal{S} = int{mathcal{L}{},d^ns},

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{}{}{}{} s_lpha denoting the set of parameters of the system.

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The equations of motion obtained by means of the functional derivative are identical to the usual Euler-Lagrange equations. A dynamical system whose equations of motion are obtainable by means of an action principle on a suitably chosen Lagrangian are known as Lagrangian dynamical systems. Examples of Lagrangian dynamical systems range from the (classical version of the) Standard Model to Newton's equations to purely mathematical problems such as geodesic equations and Plateau's problem.

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Dynamical system: A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. The mathematical models used to describe the swinging of a clock pendulum, the flow of water in a pipe, or the number of fish each spring in a lake are examples of dyna...

Joseph Louis Lagrange: Joseph Louis Lagrange (January 25, 1736 – April 10, 1813) was an Italian mathematician and astronomer who later lived in France and Prussia....

Functional: Generally, functional refers to something with and able to fulfill its purpose or function....