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

Related Topics:
Dynamical system - Joseph Louis Lagrange - Functional - Variable - Equations of motion - Action principle

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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.

Related Topics:
Set - Parameter

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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.

Related Topics:
Equations of motion - Functional derivative - Euler-Lagrange equations - Dynamical system - Action principle - Standard Model - Newton's equations - Geodesic - Plateau's problem

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