Discriminantly separable polynomials and the generalized Kowalevski top

Vladimir Dragović, Katarina Kukić

The notion of discriminantly separable polynomials of degree two in each of three variables has been recently introduced and related to a class of integrable dynamical systems. Explicit integration of such systems can be performed in a way similar to Kowalevski's original integration of the Kowalevski top. Here we present the role of discriminantly separable polynomials in integration of yet another well known integrable system, the so-called generalized Kowalevski top - the motion of a heavy rigid body about a fixed point in a double constant field. We present a novel way to obtain the separation variables for this system, based on the discriminantly separable polynomials.