Phase Space Topology and Bifurcation of Liouville Torii in the Goryatchev-Tchaplygin Top

Abstract

The classical problem of a rigid body with a fixed point is considered in the case of Goryatchev-Tchaplygin. We give a complete description of its real phase space topology. All generic bifurcation of Liouville Torii is determined theoretically and numerically. We give also explicit periodic solutions of the problem.The classical problem of a rigid body with a fixed point is considered in the case of Goryatchev-Tchaplygin. We give a complete description of its real phase space topology. All generic bifurcation of Liouville Torii is determined theoretically and numerically. We give also explicit periodic solutions of the problem

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