Using Lejbenzon ? Ishlinsky method of investigating the stability of deformable systems, forms of loss of stability of elastic fluctuations of a spherical model of the Earth of a homogeneous compressed linearly elastic material, rotating in the potential Newtonian force field caused by the Moon and the Sun, are studied. As the basic subcritical condition the compelled spheroidal fluctuations of considered model of the Earth are considered. Free fluctuations of this model are investigated. Boundary conditions stability of are assigned. The spectrum of bifurcational frequencies of fluctuations, comparable with frequency of free fluctuations is revealed. The measure of a dynamic susceptibility to compelling bifurcational forces is defined. According to this measure, it is possible to judge the resonant phenomena in the Earth, serving by the trigger mechanism for earthquakes. A numerical realization of the theory is given. Animation showing resonant splashes is created.
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