The separation of variables and bifurcations of first integrals in one problem of D.N.Goryachev

Abstract

The equations of motion in one partial integrable case of D.N.Goryachev in the rigid body dynamics are separated by the real change of variables. We obtain the Abel--Jacobi equations with the polynomial of degree 6 under the radical. The natural phase variables (components of the momentum and the momentum force) are expressed via separated variables explicitly in elementary algebraic functions. Basing on these expressions the phase topology of the system is described.