Noether symmetry method for Hamiltonian mechanics involving generalized operators
type: Item
instance of: scholarly article
title: Noether symmetry method for Hamiltonian mechanics involving generalized operators
zbMATH Open document ID: 1501.26007
DOI: 10.1155/2021/1959643
author: Chuan-Jing Song
author: Yao Cheng
published in: Advances in Mathematical Physics
publication date: 2021-11-25T00:00:00Z
review text: The Agrawal generalized operators, fractional differential operators including Riemann-Liouville, Caputo, Riesz-Riemann-Liouville and Riesz-Caputo operators, are here employed to determine generalized Hamiltonian mechanics and generalized Noether theorems. Left and right generalized operators are briefly introduced, along with the corresponding Hamilton equations. The Noether theorem is then formulated, in the Hamiltonian setting, for the left and right generalized operators, with and without gauge function. The existence of adiabatic invariants of the generalized Hamilton equations is characterized by the existence of a suitable gauge function. As examples, invariants and adiabatic invariants are determined for the 2D isotropic harmonic oscillator and the Lotka biochemical oscillator.
reviewed by: Giovanni Rastelli
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 70H33
zbMATH DE Number: 7433475
zbMATH Keywords: fractional differential operators
zbMATH Keywords: Hamilton equations
zbMATH Keywords: Noether theorem
Wikidata QID: Q114070088
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/1959643
OpenAlex ID: W3201743410
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description: scientific article; zbMATH DE number 7433475