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

@article{Lazo2019NoetherTF,
  title={Noether theorem for action-dependent Lagrangian functions: conservation laws for non-conservative systems},
  author={Matheus J. Lazo and Juilson Paiva and Gast{\~a}o S. F. Frederico},
  journal={Nonlinear Dynamics},
  year={2019},
  pages={1-12}
}
In the present work, we formulate a generalization of the Noether Theorem for action-dependent Lagrangian functions. The Noether’s theorem is one of the most important theorems for physics. It is well known that all conservation laws, e.g., conservation of energy and momentum, are directly related to the invariance of the action under a family of transformations. However, the classical Noether theorem cannot be applied to study non-conservative systems because it is not possible to formulate… 
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