This article is cited in 1 scientific paper (total in 1 paper)
Projective Dynamics and First Integrals
IMCCE-CNRS-UMR, Observatoire de Paris, 77, avenue Denfert-Rochereau, 75014 Paris, France
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.
bi-hamiltonian, Beltramiís theorem, Young tableau symmetry, free motion, force field, decomposability preserving
MSC: 70F10, 53A20
Alain Albouy, “Projective Dynamics and First Integrals”, Regul. Chaotic Dyn., 20:3 (2015), 247–276
Citation in format AMSBIB
\by Alain Albouy
\paper Projective Dynamics and First Integrals
\jour Regul. Chaotic Dyn.
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