Abstract
Evolutionary effects in the motion of a heavy dynamically symmetrical rigid body about a fixed point in cases close to the Lagrange case are investigated in the non-linear formulation. Evolutionary effects are due to perturbations acting on the body, namely, a small displacement of the centre of mass with respect to the axis of dynamic symmetry, a perturbing moment, constant in a connected system of coordinates, and dissipative moments. It is shown that the presence of perturbations leads to the existence of “attracting” or “repulsing” resonances, which determine the evolution of the system in non-resonance parts of the motion. The method of integral manifolds is used for singularly perturbed systems and the method of averaging. A qualitative representation of possible motions of a statically stable top in the phase plane, taking a lower-order resonance into account, is given.
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