An Action Principle for Action-dependent Lagrangians: toward an Action Principle to non-conservative systems

2018/03/22 by Matheus J. Lazo, Juilson Paiva, João T. S. Amaral +1 · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.MP #physics.class-ph

paper · pdf · doi:10.1063/1.5019936

published as Journal of Mathematical Physics 59, 032902 (2018)

arxiv created 2018/03/22 · arxiv updated 2018/03/23

Abstract

In this work, we propose an Action Principle for Action-dependent Lagrangian functions by generalizing the Herglotz variational problem to the case with several independent variables. We obtain a necessary condition for the extremum equivalent to the Euler-Lagrange equation and, through some examples, we show that this generalized Action Principle enables us to construct simple and physically meaningful Action-dependent Lagrangian functions for a wide range of non-conservative classical and quantum systems. Furthermore, when the dependence on the Action is removed, the traditional Action Principle for conservative systems is recovered.

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• Noether theorem for action-dependent Lagrangian functions: conservation laws for non-conservative systems

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