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Projective dynamics and first integrals

Alain Albouy
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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.

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Alain Albouy. 2006-12-11. Projective dynamics and first integrals. https://doi.org/10.1134/s1560354715030041

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