An action principle for action-dependent Lagrangians: Toward an action principle to non-conservative systems

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 example...

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Bibliographic Details
Published in:Journal of mathematical physics 2018-03, Vol.59 (3)
Main Authors: Lazo, Matheus J., Paiva, Juilson, Amaral, João T. S., Frederico, Gastão S. F.
Format: Article
Language:English
Subjects:
Differential equations
Euler-Lagrange equation
Eulers equations
Independent variables
Lagrange multiplier
Physics
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Summary: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.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.5019936