The resonance motions of a statically stable Lagrange top at small nutation angles

Abstract

The resonance motion modes of a Lagrange top with small mass asymmetry upon passage through low-order resonances are analysed. The motion of a rigid body with a prolate ellipsoid of inertia is considered in the vicinity of a lower, statically stable equilibrium position at small nutation angles. The original system of equations is reduced to the equation of motion of a pendulum with small perturbations using an averaging method. The conditions for plunging the phase trajectory of the system into oscillation regions of the pendulum, i.e., the possibility of capture into resonance under the action of the perturbations considered, are analysed. Cases in which captures into resonance are possible and in which they are not are established. Numerical calculations that illustrate the analytical estimates obtained are presented.