Projective Dynamics and First Integrals

    2015, Volume 20, Number 3, pp.  247-276

    Author(s): Albouy A.

    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
    Citation: Albouy A., Projective Dynamics and First Integrals, Regular and Chaotic Dynamics, 2015, Volume 20, Number 3, pp. 247-276

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