Conserved quantities for Hamiltonian systems on time scales

Chuan-Jing Song and Yi Zhang

Applied Mathematics and Computation, 2017, vol. 313, issue C, 24-36

Abstract: Conserved quantities for Hamiltonian systems on time scales with nabla derivatives and delta derivatives are presented. First, Hamilton principle on time scales with nabla derivatives is established and Hamilton canonical equation with nabla derivatives is obtained. Second, Noether identity and Noether theorem for Hamiltonian systems with nabla derivatives are achieved. Third, Hamilton canonical equation with delta derivatives, Noether identity and Noether theorem for Hamiltonian systems with delta derivatives are gotten through duality principle on the basis of the corresponding results with nabla derivatives. Fourth, some special cases of Noether identity and Noether theorem are given. And finally, two examples are devoted to illustrate the methods and results.

Keywords: Hamiltonian system; Conserved quantity; Time scale; Duality principle (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:313:y:2017:i:c:p:24-36

DOI: 10.1016/j.amc.2017.05.074

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