Explicit integration of one problem of motion of the generalized Kowalevski top

Details Explicit integration of one problem of motion of the generalized Kowalevski top Explicit integration of one problem of motion of the generalized Kowalevski top

2008-03-06

arxiv.org/abs/0803.0857v1

Mech. Res. Commun., 2005, N 32, pp. 547-552

Nonlinear Sciences

Exactly Solvable and Integrable Systems

6 pages

Scientific paper

10.1016/j.mechrescom.2005.02.010

In the problem of motion of the Kowalevski top in a double force field the 4-dimensional invariant submanifold of the phase space was pointed out by M.P.Kharlamov (Mekh. Tverd. Tela, 32, 2002). We show that the equations of motion on this manifold can be separated by the appropriate change of variables, the new variables s1, s2 being elliptic functions of time. The natural phase variables (components of the angular velocity and the direction vectors of the forces with respect to the movable basis) are expressed via s1, s2 explicitly in elementary algebraic functions.

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