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 Connections
Has Statement Form
In Branch
Source Herglotz's variational principle (Wikipedia)
Proved By
Source Herglotz's variational principle (Wikipedia)
Sources
1. Herglotz's variational principle (Wikipedia)
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)
In Branch: Calculus of Variations, Lead
Herglotz's variational principle, named after German mathematician and physicist Gustav Herglotz, is an extension of the Hamilton's principle
In Group: Classical Mechanics and Dynamics, Lead section
and physicist Gustav Herglotz, is an extension of the Hamilton's principle, where the Lagrangian L explicitly involves the
Proved By: Gustav Herglotz, Lead
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
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.