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This article is cited in 6 scientific papers (total in 6 papers)
Noether symmetries and integrability in time-dependent Hamiltonian mechanics
Božidar Jovanović Mathematical Institute SANU, Serbian Academy of Sciences and Arts, Belgrade, Serbia
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.
Keywords:
symmetries, the principle of stationary action, Poincaré–Cartan form, contact Hamiltonin vector fields, Noether theorem.
Received: 21.01.2016 Revised: 19.07.2016
Citation:
Božidar Jovanović, “Noether symmetries and integrability in time-dependent Hamiltonian mechanics”, Theor. Appl. Mech., 43:2 (2016), 255–273
Linking options:
https://www.mathnet.ru/eng/tam16 https://www.mathnet.ru/eng/tam/v43/i2/p255
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Abstract page: | 82 | Full-text PDF : | 37 | References: | 23 |
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