Rigid body dynamics in non-Euclidean spaces

DOI10.1134/S1061920816040026zbMath1406.70009WikidataQ125803668 ScholiaQ125803668MaRDI QIDQ519746

Ivan. S. Mamaev, Alexey V. Borisov

Publication date: 5 April 2017

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Mathematics Subject Classification ID

Free motion of a rigid body (70E15)

Related Items (9)

Integrable systems on a sphere, an ellipsoid and a hyperboloid ⋮ First Appelrot class of pseudo-Euclidean Kovalevskaya system ⋮ Dynamics of constrained many body problems in constant curvature two-dimensional manifolds ⋮ Noncompactness property of fibers and singularities of non-Euclidean Kovalevskaya system on pencil of Lie algebras ⋮ Reduction and relative equilibria for the two-body problem on spaces of constant curvature ⋮ A note about integrable systems on low-dimensional Lie groups and Lie algebras ⋮ Bifurcation analysis of the dynamics of two vortices in a Bose-Einstein condensate. the case of intensities of opposite signs ⋮ On the Chaplygin sphere in a magnetic field ⋮ Lambert's theorem and projective dynamics

Cites Work

• Stability of equilibria for the \(\mathfrak{so}(4)\) free rigid body
• Stability in bihamiltonian systems and multidimensional rigid body
• Dynamical invariants of rigid motions on the hyperbolic plane
• Die Dynamik des starren Körpers in einem nichteuklidischen Raum
• Euler equations in the algebras e(3) and so(4). Isomorphisms of integrable cases
• Bifurcation set and integral manifolds of the problem concerning the motion of a rigid body in a linear force field
• On the dynamics of a rigid body in the hyperbolic space
• Two-body problem on a sphere. Reduction, stochasticity, periodic orbits
• The spatial problem of 2 bodies on a sphere. Reduction and stochasticity
• Topology and stability of integrable systems
• Algebraic constructions of integrable dynamical systems-extensions of the Volterra system
• SOME REMARKS ON THE MOTION OF A RIGID BODY IN A SPACE OF CONSTANT CURVATURE WITHOUT EXTERNAL FORCES1
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