Separation of variables on non-hiperelliptic curve

V. G. Marikhin, V. V. Sokolov

L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Abstract: A 8-parametric pair of commuting Hamiltonians of two degrees of freedom, quadratic in moments and coefficients depending only on coordinates is constructed. The Schottky-Manakov and the Clebsch spinning tops are particular cases of this model. The action function as an integral on a non-hyperelliptic curve of genus 4 is found.

Keywords: Action function, separation of variables, covering of an elliptic curve.

UDC: 531.3