The Orbital Stability Analysis of Pendulum Oscillations of a Heavy Rigid Body with a Fixed Point Under the Goriachev–Chaplygin Condition

We consider the motion of a heavy rigid body with a fixed point in a uniform gravitational field under the assumption that the principal moments of inertia satisfy the Goryachev–Chaplygin condition at the fixed point. We study the orbital stability problem for small pendulum oscillations of the body. We derive the equations of perturbed motion and reduce the problem to the study of the stability of the equilibrium position of a second order 2π-periodic Hamiltonian system. We find regions of parametric resonance and perform the nonlinear analysis of orbital stability outside these regions. © 2023, Springer Nature Switzerland AG.