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We consider a spherical pendulum whose suspension point performshigh-frequency spatial vibrations. Dynamics of this pendulum can be describedby averaging of its Hamiltonian over phases of vibrations. We impose conditionson vibrations such that that the averaged Hamiltonian has a rotationalsymmetry. Under these conditions we present a bifurcation diagram for the phaseportraits of the averaged system. We show numerical simulations of differentexamples of vibrations. Bifurcation of phase portraits of spherical physicalpendulum with vibrating suspension point are considered as well.

Bifurcations of phase portraits of spherical pendulum with vibrating suspension point