Geodesic
Separation of variables on non-hiperelliptic curve
Russian journal of nonlinear dynamics, Tome 1 (2005) no. 1, pp. 53-67.

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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. 
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V. G. Marikhin; V. V. Sokolov. Separation of variables on non-hiperelliptic curve. Russian journal of nonlinear dynamics, Tome 1 (2005) no. 1, pp. 53-67. http://geodesic.mathdoc.fr/item/ND_2005_1_1_a3/