The three-body problem in Riemannian geometry. Hidden irreversibility of the classical dynamical system

DOI10.1134/S1995080219080080zbMath1459.70027OpenAlexW2971894633WikidataQ115247374 ScholiaQ115247374MaRDI QIDQ2010157

A. S. Gevorkyan

Publication date: 3 December 2019

Published in: Lobachevskii Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1995080219080080

zbMATH Keywords

three-body problemRiemannian manifolddynamical systemgeodesic equationsirreversible equations systemunderdetermined algebraic system

Mathematics Subject Classification ID

Three-body problems (70F07) Differential geometric aspects in kinematics (53A17) Dynamical systems in classical and celestial mechanics (37N05) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Cites Work

• Hamiltonian dynamics of atom-diatomic molecule complexes and collisions
• The restricted three-body problem: plane periodic orbits. Transl. from the Russian by Balint Erdi. With a preface by Victor G. Szebehely
• Symplectic reduction, geometric phase, and internal dynamics in three-body molecular dynamics.
• Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
• The Three-Body Problem
• General properties of three-body systems with Hill-type stability
• Use of alternative hyperspherical coordinates for three-body systems
• A Treatise on the Analytical Dynamics of Particles and Rigid Bodies
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