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Integrable billiards model important integrable cases of rigid body dynamics

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Abstract—A generalized billiard is considered, in which a point moves on a locally flat surface obtained by isometrically gluing together several plane domains along boundaries being arcs of confocal quadrics. Under this motion, a point moves from one domain to another, passing through the glued boundaries. Many integrable cases of rigid body dynamics with appropriate parameter values at certain levels of integrals are modeled by classical or generalized billiards; in the paper, Liouville equivalence is proved by comparing Fomenko–Zieschang invariants.

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Authors and Affiliations

  1. Mechanics and Mathematics Faculty, Moscow State University, Moscow, 119991, Russia

    V. V. Fokicheva & A. T. Fomenko

Authors
  1. V. V. Fokicheva
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  2. A. T. Fomenko
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Correspondence to V. V. Fokicheva.

Additional information

Original Russian Text © V.V. Fokicheva, A.T. Fomenko, 2015, published in Doklady Akademii Nauk, 2015, Vol. 465, No. 2, pp. 150–153.

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Fokicheva, V.V., Fomenko, A.T. Integrable billiards model important integrable cases of rigid body dynamics. Dokl. Math. 92, 682–684 (2015). https://doi.org/10.1134/S1064562415060095

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