Authors: Jovanović, Božidar 
Title: Noether symmetries and integrability in time-dependent hamiltonian mechanics
Journal: Theoretical and Applied Mechanics
Volume: 43
Issue: 2
First page: 255
Last page: 273
Issue Date: 1-Jan-2016
Rank: M24
ISSN: 1450-5584
DOI: 10.2298/TAM160121009J
We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincaŕe-Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms. In the case when the Poincaŕe-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.
Keywords: Contact hamiltonin vector fields | Noether theorem | Poincaré-Cartan form | Symmetries | The principle of stationary action
Publisher: Serbian Society for Mechanics
Project: Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems 

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