Noether symmetries and integrability in time-dependent Hamiltonian mechanics

Abstract

We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincaré-Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms. In the case when the Poincaré-Cartan form is contact, the explicit expression for the symmetries in the inverse Noether theorem is given. As examples, we consider natural mechanical systems, in particular the Kepler problem. Finally, we prove a variant of the theorem on complete (non-commutative) integrability in terms of Noether symmetries of time-dependent Hamiltonian systems.

18 pages, 2 figures, to appear in Theoretical and Applied Mechanics

References in corpus (2)

• Noether's theorem and Lie symmetries for time-dependent Hamilton-Lagrange systems
• Lie algebras of conservation laws of variational ordinary differential equations