Equilibria, stability and Hamiltonian Hopf bifurcation of a gyrostat in an incompressible ideal fluid

DOI10.1016/j.physd.2012.07.003zbMath1251.70005OpenAlexW1968036465MaRDI QIDQ1758251

Juan A. Vera, Juan Luis García Guirao

Publication date: 8 November 2012

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2012.07.003

zbMATH Keywords

stabilityrelative equilibriaKirchhoff equationsenergy-Casimir methodHamiltonian Hopf bifurcationLie-Poisson systems

Mathematics Subject Classification ID

Motion of the gyroscope (70E05)

Related Items (4)

On the stability of the permanent rotations of a charged rigid body-gyrostat ⋮ Periodic solutions induced by an upright position of small oscillations of a sleeping symmetrical gyrostat ⋮ Control of the motion of a triaxial ellipsoid in a fluid using rotors ⋮ Hamiltonian structure, equilibria, and stability for an axisymmetric gyrostat motion in the presence of gravity and magnetic fields

Cites Work

• Nonlinear stability of the equilibria in a double-bar rotating system
• On the Hamiltonian Hopf bifurcations in the 3D Hénon-Heiles family
• Dynamics of the Kirchhoff equations. I: Coincident centers of gravity and buoyancy
• The Hamiltonian Hopf bifurcation
• Stability of a bottom-heavy underwater vehicle
• Nonlinear stability of fluid and plasma equilibria
• Lagrangian relative equilibria for a gyrostat in the three-body problem: bifurcations and stability
• Stability of Hamiltonian relative equilibria
• Sufficient conditions for a nondegenerate Hopf bifurcation in a generalized Lagrange–Poisson problem
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