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Theoretical and Applied Mechanics, 2016, Volume 43, Issue 2, Pages 255–273
DOI: https://doi.org/10.2298/TAM160121009J
(Mi tam16)
 

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
Full-text PDF (279 kB) Citations (6)
References:
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.
Funding agency Grant number
Ministry of Education, Science and Technical Development of Serbia 174020
The research was supported by the Serbian Ministry of Science Project 174020, Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems.
Received: 21.01.2016
Revised: 19.07.2016
Bibliographic databases:
Document Type: Article
Language: English
Citation: Božidar Jovanović, “Noether symmetries and integrability in time-dependent Hamiltonian mechanics”, Theor. Appl. Mech., 43:2 (2016), 255–273
Citation in format AMSBIB
\Bibitem{Jov16}
\by Bo{\v z}idar~Jovanovi{\'c}
\paper Noether symmetries and integrability in time-dependent Hamiltonian mechanics
\jour Theor. Appl. Mech.
\yr 2016
\vol 43
\issue 2
\pages 255--273
\mathnet{http://mi.mathnet.ru/tam16}
\crossref{https://doi.org/10.2298/TAM160121009J}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000391372600006}
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  • https://www.mathnet.ru/eng/tam16
  • https://www.mathnet.ru/eng/tam/v43/i2/p255
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Theoretical and Applied Mechanics
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    Full-text PDF :37
    References:23
     
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