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.

arXiv comment18 pages, 2 figures, to appear in Theoretical and Applied Mechanics

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• Contact flows and integrable systems
• Unified formalism for non-autonomous mechanical systems
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Cited by in corpus (5)

• Infinitesimal symmetries in Contact Hamiltonian systems
• Moving energies as first integrals of nonholonomic systems with affine constraints
• Rolling balls over spheres in R^n
• Integrable systems in cosymplectic geometry
• Nonholonomic connections, time reparametrizations, and integrability of the rolling ball over a sphere