Symmetries and first integrals for variational ODEs with delay
Mathematical Physics
2023-03-17 v1 math.MP
Abstract
A Lagrangian formalism for variational second-order delay ordinary differential equations (DODEs) is developed. The Noether operator identity for a DODE is established, which relates the invariance of a Lagrangian function with the appropriate variational equations and the conserved quantities. The identity is used to formulate Noether-type theorems that give the first integrals for DODE with symmetries. Relations between the invariance of the variational second-order DODEs and the invariance of the Lagrangian functions are also analyzed. Several examples illustrate the theoretical results.
Cite
@article{arxiv.2303.09102,
title = {Symmetries and first integrals for variational ODEs with delay},
author = {V. A. Dorodnitsyn and R. V. Kozlov and S. V. Meleshko},
journal= {arXiv preprint arXiv:2303.09102},
year = {2023}
}