Resonant Motions of the Statically Stable Lagrangian Top
The resonances of the lower orders at the movement of the Lagrange top with small mass asymmetry are analyzed. The conditions for the realization of long resonance regimes in linear and nonlinear cases using of averaging and method of integral manifolds are compared. The motion of a heavy solid body with an elongated ellipsoid of inertia in the vicinity of the lower statically stable equilibrium position is considered. A theorem justifying the application of the method of integral manifolds for non-small nutation angles when a rigid body moves around a fixed point is given. The resonance capture conditions in the nonlinear case for nutation angles not exceeding <inline-formula><inline-graphic href="PrMatM1904016Zabolotnov-m2" xmlns:xlink="http://www.w3.org/1999/xlink"></inline-graphic></inline-formula> are obtained. Numerical examples illustrating the effect of nonlinearities on the resonance motion of the Lagrange top are considered.