Herglotz's variational principle, named after the German mathematician and physicist Gustav Herglotz, extends Hamilton's principle in mathematical physics by allowing the Lagrangian to depend on the action itself as an independent variable, so that the action is obtained as the solution of an ordinary differential equation rather than as a straightforward integral of the Lagrangian. The principle grew out of contact geometry and applies to nonconservative Lagrangian and Hamiltonian systems, including ones with dissipation, that Hamilton's original principle cannot describe.
Facts
StatementHerglotz's variational principle is an extension of Hamilton's principle where the Lagrangian explicitly involves the action as an independent variable, represented as the solution of an ordinary differential equation instead of an integration. 1 Classification
Statement FormCharacterization Theorem 1 Sources
1. Herglotz's variational principle (Wikipedia)
IntroductionQuote, Introduction
is an extension of the Hamilton's principle, where the Lagrangian L explicitly involves the action S as an independent variable, and S itself is represented as the solution of an ordinary differential equation (ODE)
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