Reducing the degree of integrals of Hamiltonian systems by using billiards

DOI10.1134/S1064562419030086zbMath1423.37055OpenAlexW2965673075MaRDI QIDQ2332083

A. T. Fomenko, V. V. Vedyushkina

Publication date: 1 November 2019

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562419030086

zbMATH Keywords

integrable rigid body dynamicsconfocal quadrics

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Integrable cases of motion in rigid body dynamics (70E40)

Related Items (6)

Topological analysis of an elliptic billiard in a fourth-order potential field ⋮ Topological classification of integrable geodesic billiards on quadrics in three-dimensional Euclidean space ⋮ Billiards with changing geometry and their connection with the implementation of the Zhukovsky and Kovalevskaya cases ⋮ Billiards and integrable systems ⋮ Billiard with slipping at any rational angle ⋮ The Liouville foliation of the billiard book modelling the Goryachev-Chaplygin case

Cites Work

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• Integrable billiards model important integrable cases of rigid body dynamics
• Classification of the family of Kovalevskaya-Yehia systems up to Liouville equivalence
• Modeling nondegenerate bifurcations of closures of solutions for integrable systems with two degrees of freedom by integrable topological billiards
• Integrable geodesic flows on the sphere, generated by Goryachev-Chaplygin and Kowalewski systems in the dynamics of a rigid body
• Topology of the Liouville foliation on a 2-sphere in the Dullin-Matveev integrable case
• Topology of Liouville foliations in the Steklov and the Sokolov integrable cases of Kirchhoff's equations
• The Maupertuis principle and geodesic flows on the sphere arising from integrable cases in the dynamics of a rigid body
• The Fomenko-Zieschang invariants of nonconvex topological billiards

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