Bifurcations of phase portraits of spherical pendulum with vibrating suspension point. (arXiv:1708.01313v1 [math.GM])

We consider a spherical pendulum whose suspension point performs high-frequency oscillations. We derive the averaged over these oscillations Hamiltonian of the problem. We assume that these oscillations are such that the averaged Hamiltonian is invariant with respect to rotations about the vertical direction. Under this assumption we give complete description of bifurcations of phase portraits of the averaged system. 查看全文>>