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Regul. Chaotic Dyn., 2015, Volume 20, Issue 3, Pages 247–276 (Mi rcd42)  

This article is cited in 1 scientific paper (total in 1 paper)

Projective Dynamics and First Integrals

Alain Albouy

IMCCE-CNRS-UMR, Observatoire de Paris, 77, avenue Denfert-Rochereau, 75014 Paris, France

Abstract: We present the theory of tensors with Young tableau symmetry as an efficient computational tool in dealing with the polynomial first integrals of a natural system in classical mechanics. We relate a special kind of such first integrals, already studied by Lundmark, to Beltramiís theorem about projectively flat Riemannian manifolds. We set the ground for a new and simple theory of the integrable systems having only quadratic first integrals. This theory begins with two centered quadrics related by central projection, each quadric being a model of a space of constant curvature. Finally, we present an extension of these models to the case of degenerate quadratic forms.

Keywords: bi-hamiltonian, Beltramiís theorem, Young tableau symmetry, free motion, force field, decomposability preserving

DOI: https://doi.org/10.1134/S156035471503004

References: PDF file   HTML file

Bibliographic databases:

MSC: 70F10, 53A20
Received: 02.02.2015
Language:

Citation: Alain Albouy, “Projective Dynamics and First Integrals”, Regul. Chaotic Dyn., 20:3 (2015), 247–276

Citation in format AMSBIB
\Bibitem{Alb15}
\by Alain Albouy
\paper Projective Dynamics and First Integrals
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 3
\pages 247--276
\mathnet{http://mi.mathnet.ru/rcd42}
\crossref{https://doi.org/10.1134/S156035471503004}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3357275}
\zmath{https://zbmath.org/?q=an:06488656}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2015RCD....20..247A}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Miguel A. Gonzalez Leon, Juan Mateos Guilarte, Marina de la Torre Mayado, “Orbits in the Problem of Two Fixed Centers on the Sphere”, Regul. Chaotic Dyn., 22:5 (2017), 520–542  mathnet  crossref
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