Resonant Motions of the Statically Stable Lagrange Spinning Top

Abstract

In this paper, we analyze lower-order resonances during the motion of the Lagrange spinning top with a small mass asymmetry. The conditions for the implementation of long resonance modes obtained by both the averaging method in the linear case and the method of integral manifolds for considerable nutation angles are compared. The motion of a heavy rigid body with an elongated inertia ellipsoid is considered in the vicinity of the lower statically stable equilibrium position. We present a theorem that justifies the application of the method of integral manifolds for considerable nutation angles when a rigid body moves around a fixed point. The resonance capture conditions in the nonlinear case are estimated for nutation angles not exceeding ρ/2. Numerical examples illustrating the effect of nonlinearities on the resonant motion of the Lagrange spinning top are considered.