Topological analysis corresponding to the Borisov-Mamaev-Sokolov integrable system on the Lie algebra \(\mathrm{so}(4)\)

DOI10.1134/S1560354716010019zbMath1337.37039WikidataQ115247423 ScholiaQ115247423MaRDI QIDQ283023

Rasoul Akbarzadeh

Publication date: 13 May 2016

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

zbMATH Keywords

topologybifurcation diagramintegrable Hamiltonian systemscritical setbifurcation complexisoenergy surfacesperiodic trajectory

Mathematics Subject Classification ID

Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems (37J20) Bifurcations and instability for nonlinear problems in mechanics (70K50) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Topological and differential topological methods for problems in mechanics (70G40)

Related Items (5)

Explicit integration of the system of invariant relations for the case of M. Adler and P. van Moerbeke ⋮ On one approach to the qualitative analysis of nonlinear dynamical systems ⋮ Explicit determination of certain periodic motions of a generalized two-field gyrostat ⋮ The topology of isoenergetic surfaces for the Borisov-Mamaev-Sokolov integrable case on the Lie algebra \(so(3, 1)\) ⋮ The integrable case of Adler-van Moerbeke. Discriminant set and bifurcation diagram

Cites Work

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• Topological analysis of an integrable system related to the rolling of a ball on a sphere
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• Topological invariants of Liouville integrable Hamiltonian systems
• Bifurcation sets in a problem on motion of a rigid body in fluid and in the generalization of this problem
• A new integrable case for the Kirchhoff equation
• One class of quadratic \(\mathrm{so}(4)\) Hamiltonians
• The dynamics of nonholonomic systems consisting of a spherical shell with a moving rigid body inside
• Bifurcations of first integrals in the Sokolov case
• Topology and stability of integrable systems
• The method of loop molecules and the topology of the Kovalevskaya top

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