English

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

Mathematical Physics 2018-03-23 v1 math.MP Classical Physics

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.

Keywords

Cite

@article{arxiv.1803.08308,
  title  = {An Action Principle for Action-dependent Lagrangians: toward an Action Principle to non-conservative systems},
  author = {Matheus J. Lazo and Juilson Paiva and João T. S. Amaral and Gastão S. F. Frederico},
  journal= {arXiv preprint arXiv:1803.08308},
  year   = {2018}
}