Phase Space Topology and Bifurcation of Liouville Torii in the Goryatchev-Tchaplygin Top
نویسندگان
چکیده
The problem of the motion, of a rigid body around a fixed point, in the field of constant gravity, is one of the oldest in mechanics [1,2,3]. The problem can be formulated in terms of a timeindependent Hamiltonian with three degrees of freedom (the Euler angles. In addition to the energy constant, there is present another constant of motion: the angular momentum component along the vertical. Rotation around the vertical is a cyclic coordinate in the Hamiltonian, which produces the new constant and allows the reduction of the problem to only two degrees of freedom. The equations of motion (Euler-Poisson equations) are given by:
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