First Noether-type theorem for the generalized variational principle of Herglotz

Abstract

In this paper we formulate and prove a theorem, which provides the
conserved quantities of a system described by the generalized variational
principle of Herglotz.
This new theorem contains as a special case the classical first Noether theorem.
It reduces to it when the generalized variational principle of Herglotz reduces
to the classical variational principle.
Several examples for applications to physics are given.