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This article is cited in 4 scientific papers (total in 4 papers)
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 Beltrami’s 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, Beltrami’s theorem, Young tableau symmetry, free motion, force field, decomposability preserving.
Received: 02.02.2015
Citation:
Alain Albouy, “Projective Dynamics and First Integrals”, Regul. Chaotic Dyn., 20:3 (2015), 247–276
Linking options:
https://www.mathnet.ru/eng/rcd42 https://www.mathnet.ru/eng/rcd/v20/i3/p247
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Abstract page: | 193 | References: | 41 |
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