The pendulum-like motions of a rigid body in the Goryachev-Chaplygin case

DOI10.1016/S0021-8928(04)90024-XzbMath1150.70313MaRDI QIDQ5318190

Anatoliy P. Markeev

Publication date: 21 September 2005

Published in: Journal of Applied Mathematics and Mechanics (Search for Journal in Brave)

zbMATH Keywords

solidGoryachev-Chaplygin rotation casependulum-like oscillations

Mathematics Subject Classification ID

Stability problems in rigid body dynamics (70E50) Integrable cases of motion in rigid body dynamics (70E40) Motion of a rigid body with a fixed point (70E17)

Related Items (10)

Invariant sets in the Goryachev–Chaplygin problem: existence, stability and branching ⋮ Asymptotically uniform motions of a gyrostat about an inclined axis under potential and gyroscopic forces ⋮ The orbital stability analysis of pendulum oscillations of a heavy rigid body with a fixed point under the Goryachev-Chaplygin condition ⋮ The stability of the plane periodic motions of a symmetrical rigid body with a fixed point ⋮ On the orbital stability of planar periodic motions of a rigid body in the Bobylev-Steklov case ⋮ On the orbital stability of pendulum-like vibrations of a rigid body carrying a rotor ⋮ On a class of solutions for the dynamic equations of a rigid body acted upon by potential and gyroscopic forces ⋮ The dynamical motion of a gyrostat for the irrational frequency case ⋮ Integrable variational equations of non-integrable systems ⋮ On the Stability of Pendulum-type Motions in the Approximate Problem of Dynamics of a Lagrange Top with a Vibrating Suspension Point

Cites Work

• The critical case of fourth-order resonance in a hamiltonian system with one degree of freedom
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