The spatial problem of 2 bodies on a sphere. Reduction and stochasticity

DOI10.1134/S1560354716050075zbMath1402.70015OpenAlexW2530040191MaRDI QIDQ2520098

Alexey V. Borisov, Ivan. A. Bizyaev, Ivan. S. Mamaev

Publication date: 13 December 2016

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1560354716050075

zbMATH Keywords

rigid body dynamicsreductionPoincaré sectioncelestial mechanicsspace of constant curvature

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) Two-body problems (70F05) Celestial mechanics (70F15) History of mathematics in the 19th century (01A55) Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems (70-02) History of mechanics of particles and systems (70-03)

Related Items (21)

Equilibrium points in restricted problems on S2 and H2 ⋮ Attracting and repelling 2-body problems on a family of surfaces of constant curvature ⋮ Three-body relative equilibria on \(\mathbb{S}^2\) ⋮ Secular dynamics for curved two-body problems ⋮ Orbits in the problem of two fixed centers on the sphere ⋮ Local regularization of a restricted problem on \(H^2\) with primaries on hyperbolic motion ⋮ Explicit determination of certain periodic motions of a generalized two-field gyrostat ⋮ On certain integrable and superintegrable weight-homogeneous Hamiltonian systems ⋮ Relative equilibria for the positive curved \(n\)-body problem ⋮ Dynamics of constrained many body problems in constant curvature two-dimensional manifolds ⋮ Non-integrability of the Kepler and the two-body problems on the Heisenberg group ⋮ Rigid body dynamics in non-Euclidean spaces ⋮ Reduction and relative equilibria for the two-body problem on spaces of constant curvature ⋮ Dynamics on the double Morse potential: a paradigm for roaming reactions with no saddle points ⋮ Stability of the polar equilibria in a restricted three-body problem on the sphere ⋮ Singular reduction of the 2-body problem on the 3-sphere and the 4-dimensional spinning top ⋮ Continuation of relative equilibria in the \(n\)-body problem to spaces of constant curvature ⋮ On the Equivalence Between Type I Liouville Dynamical Systems in the Plane and the Sphere ⋮ Hyperbolic regularization of the restricted three-body problem on curved spaces ⋮ Point mass dynamics on spherical hypersurfaces ⋮ Lambert's theorem and projective dynamics

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