Separation of variables in the generalized 4th Appelrot class

Details Separation of variables in the generalized 4th Appelrot class Separation of variables in the generalized 4th Appelrot class

2008-03-07

arxiv.org/abs/0803.1024v1

Regular and Chaotic Dynamics, 2007, Vol. 12, No. 3, pp. 267-280

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTex, 16 pages, 1 figure

Scientific paper

10.1134/S1560354707030021

We consider the analogue of the 4th Appelrot class of motions of the Kowalevski top for the case of two constant force fields. The trajectories of this family fill the four-dimensional surface O^4 in the six-dimensional phase space. The constants of three first integrals in involution restricted to this surface fill one of the sheets of the bifurcation diagram in R^3. We point out the pair of partial integrals to obtain the explicit parametric equations of this sheet. The induced system on O^4 is shown to be Hamiltonian with two degrees of freedom having the thin set of points where the induced symplectic structure degenerates. The region of existence of motions in terms of the integral constants is found. We provide the separation of variables on O^4 and the algebraic formulae for the initial phase variables.

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