Vladimir Marikhin

2, Kosygina str., 119334 Moscow, Russia
Landau Institute for Theoretical Physics of RAS


Marikhin V. G., Sokolov V. V.
In the case of two degrees of freedom the simultaneous diagonalization of pairs of Hamiltonians quadratic on momenta that commute with respect to the standard Poisson bracket is considered. A general scheme of partial separation of variables for such pairs is discussed. As an example the Clebsch top is considered.
Keywords: separation of variables, the Clebsch top
Citation: Marikhin V. G., Sokolov V. V.,  Transformation of a pair of commuting Hamiltonians quadratic in momenta to canonical form and real partial separation of variables for the Clebsch top, Regular and Chaotic Dynamics, 2010, vol. 15, no. 6, pp. 652-658
Marikhin V. G., Sokolov V. V.
Separation of variables on a non-hyperelliptic curve
2005, vol. 10, no. 1, pp.  59-70
In the paper we consider several dynamical systems that admit a separation of variables on the algebraic curve of genus 4. The main result of the paper is an explicit formula for the action of these systems. It is obtained directly from the Hamilton–Jacobi equation. We find the action and a separation of variables for the Clebsch and the $so(4)$ Schottky–Manakov spinning tops.
Keywords: integrable tops, separation of variables, Hamilton–Jacobi equation
Citation: Marikhin V. G., Sokolov V. V.,  Separation of variables on a non-hyperelliptic curve , Regular and Chaotic Dynamics, 2005, vol. 10, no. 1, pp. 59-70
DOI: 10.1070/RD2005v010n01ABEH000300

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