Discriminantly separable polynomials and the generalized Kowalevski top

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.

STABILITY, PERIODIC SOLUTIONS AND NUMERICAL INTEGRATION IN THE KOWALEVSKI TOP DYNAMICS

The stability problem, the existence of periodic solutions, the Lax formulation and the numerical integration via the Lie–Trotter integrator of the Kowalevski top dynamics are discussed, and some of their properties are pointed out.