Separation of variables in one problem of motion of the generalized Kowalevski top

In the problem of motion of the Kowalevski top in a double force field the new case of reduction to a Hamiltonian system with two degrees of freedom was pointed out by Kharlamov [Kharlamov, M.P., 2004. Mekh. Tverd. Tela 34, 47–58]. We show that the equations of motion in this case can be separated by the appropriate change of variables, the new variables U,V being hyperelliptic 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 U,V explicitly in elementary algebraic functions.