Geometric properties of integrable Kepler and Hooke billiards with conic section boundaries

DOI10.1016/J.GEOMPHYS.2024.105289MaRDI QIDQ6610204

Lei Zhao, D. Jaud

Publication date: 25 September 2024

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

zbMATH Keywords

billiardsKepler problemcentral potentialCassini ovalsHooke problemfoci curves

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Two-body problems (70F05) Geodesics in global differential geometry (53C22) Relationships between algebraic curves and integrable systems (14H70) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39) Dynamical systems with singularities (billiards, etc.) (37C83)

Cites Work

• Poncelet property and quasi-periodicity of the integrable Boltzmann system
• Les transformations isogonales en mécanique.
• The solution of a mechanical problem.
• Elliptical billiard table with Newtonian potential
• Projective dynamics and an integrable Boltzmann billiard model
• An ellipsoidal billiard with a quadratic potential
• Gravitational billiards bouncing inside general domains -- foci curves and confined domains
• Projective integrable mechanical billiards
• Chaotic dynamics in refraction galactic billiards
• Conformal transformations and integrable mechanical billiards

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