Billiard Systems as the Models for the Rigid Body Dynamics

DOI10.1007/978-3-319-40673-2_2zbMath1362.70005OpenAlexW2512660443MaRDI QIDQ2977708

A. T. Fomenko, V. V. Vedyushkina

Publication date: 19 April 2017

Published in: Advances in Dynamical Systems and Control (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-40673-2_2

Mathematics Subject Classification ID

Related Items (13)

Liouville classification of integrable geodesic flows on a torus of revolution in a potential field ⋮ Billiards bounded by arcs of confocal quadrics on the Minkowski plane ⋮ Topological classification of integrable geodesic flows in a potential field on the torus of revolution ⋮ An elliptic billiard in a potential force field: classification of motions, topological analysis ⋮ Liouville classification of integrable geodesic flows in a potential field on two-dimensional manifolds of revolution: the torus and the Klein bottle ⋮ Algorithmic construction of two-dimensional singular fibers of atoms of billiards in non-convex domains ⋮ Topology of Liouville foliations for integrable billiards in non-convex domains ⋮ Partially symmetric height atoms ⋮ Liouville foliation of topological billiards in the Minkowski plane ⋮ Topological analysis of a billiard in elliptic ring in a potential field ⋮ Three-Dimensional Manifolds of Constant Energy and Invariants of Integrable Hamiltonian Systems ⋮ Singularities of integrable Liouville systems, reduction of integrals to lower degree and topological billiards: Recent results ⋮ Topological billiards, conservation laws and classification of trajectories

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Integrable billiards model important integrable cases of rigid body dynamics
• Topological invariants of Liouville integrable Hamiltonian systems
• Orbital classification of geodesic flows on two-dimensional ellipsoids. The Jacobi problem is orbitally equivalent to the integrable Euler case in rigid body dynamics
• Description of singularities for billiard systems bounded by confocal ellipses or hyperbolas
• Orbital classification of the integrable problems of Lagrange and Goryachev-Chaplygin by the methods of computer analysis
• Topological classification of systems of Kovalevskaya-Yehia type
• THE TOPOLOGY OF SURFACES OF CONSTANT ENERGY IN INTEGRABLE HAMILTONIAN SYSTEMS, AND OBSTRUCTIONS TO INTEGRABILITY
• ON TYPICAL TOPOLOGICAL PROPERTIES OF INTEGRABLE HAMILTONIAN SYSTEMS
• THE TOPOLOGY OF INTEGRAL SUBMANIFOLDS OF COMPLETELY INTEGRABLE HAMILTONIAN SYSTEMS
• Constant energy surfaces of Hamiltonian systems, enumeration of three-dimensional manifolds in increasing order of complexity, and computation of volumes of closed hyperbolic manifolds
• Topology of Liouville foliations in the Steklov and the Sokolov integrable cases of Kirchhoff's equations

This page was built for publication: Billiard Systems as the Models for the Rigid Body Dynamics