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| The Chaplygin case (1903) of the problem of rigid body motion in fluid was generalized by D.N.Goryachev (1916) to the problem with
the potential that has a singularity in the equatorial plane of the inertia ellipsoid.
In this talk we represent the results on the phase topology of particular case of D.N.Goryachev integrability.
To study the phase topology for the Goryachev case, we use the explicit real separation of variables. This fact helped us to obtain the explicit form of the Abel-Jacobi equations with the sixth power polynomial under the radical and the algebraic expression of all phase variables in terms of real separated variables. The analytic formulas obtained allow us to study phase topology, in particular, bifurcations of Liouville tori. The investigation is carried out with the help of the method of Boolean functions developed by M.P.Kharlamov for algebraically separable systems. We found the bifurcation diagram of the moment mapping and calculate the Fomenko invariant which makes it possible to classify the system up to rough Liouville equivalence. |
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