Discriminantly separable polynomials and the generalized Kowalevski top

• Main Authors: Dragović Vladimir, Kukić Katarina
• Format: Article
• Language: English
• Published: Serbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade 2017-01-01
• Series: Theoretical and Applied Mechanics
• Subjects: the generalized Kowalevski top; discriminantly separable polynomials; separation variables
• Online Access: http://www.doiserbia.nb.rs/img/doi/1450-5584/2017/1450-55841700016D.pdf

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. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. 174020]