Herglotz's variational principle

In mathematics and physics, Herglotz's variational principle, named after German mathematician and physicist Gustav Herglotz, is an extension of the Hamilton's principle, where the Lagrangian L explicitly involves the action S {\displaystyle S} as an independent variable, and S {\displaystyle S} itself is represented as the solution of an ordinary differential equation (ODE) whose right hand side is the Lagrangian L {\displaystyle L} , instead of an integration of L {\displaystyle L} . Herglotz's variational principle is known as the variational principle for nonconservative Lagrange equations and Hamilton equations.

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Herglotz's variational principle

In mathematics and physics, Herglotz's variational principle, named after German mathematician and physicist Gustav Herglotz, is an extension of the Hamilton's principle, where the Lagrangian L explicitly involves the action S {\displaystyle S} as an independent variable, and S {\displaystyle S} itself is represented as the solution of an ordinary differential equation (ODE) whose right hand side is the Lagrangian L {\displaystyle L} , instead of an integration of L {\displaystyle L} . Herglotz's variational principle is known as the variational principle for nonconservative Lagrange equations and Hamilton equations.

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Source: Wikipedia "Herglotz's variational principle" · CC BY-SA 4.0

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