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

Bogdana Georgieva, Ronald B. Guenther


The generalized variational principle of Herglotz defines the functional,
whose extrema are sought, by a differential equation rather than by
an integral. For such functionals the classical Noether theorems are
not applicable. First and second Noether-type theorems which do apply
to the generalized variational principle of Herglotz were formulated
and proved. These theorems contain the classical first and second Noether
theorems as special cases. We published the first Noether-type theorem
previously in this journal. Here we prove the second Noether-type theorem
and show that it reduces to the classical second Noether theorem when the
Herglotz variational principle reduces to the classical variational principle.


Noether's theorems; variational principles; conserved quantities

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