Separation of variables on non-hiperelliptic curve
Copyright policy )Separation of variables on non-hiperelliptic curve
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. We find it directly from the Hamilton-Jacobi equation. We find the action and a separation of variables for the Kowalewski hyrostat, the Clebsch and the so(4) Schottky-Manakov spinning tops.
16 pages
- Landau Institute for Theoretical Physics Russian Federation
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, covering of elliptic curve, Algebraic geometry methods for problems in mechanics, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Analytic theory of abelian varieties; abelian integrals and differentials, separation of variables, integrable tops, FOS: Physical sciences, Relations of finite-dimensional Hamiltonian and Lagrangian systems with algebraic geometry, complex analysis, special functions, Mathematical Physics (math-ph), Dynamical Systems (math.DS), Hamilton-Jacobi equation, action function, Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics, Integrable cases of motion in rigid body dynamics, FOS: Mathematics, Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions, Relationships between algebraic curves and integrable systems, Mathematics - Dynamical Systems, Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, covering of elliptic curve, Algebraic geometry methods for problems in mechanics, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Analytic theory of abelian varieties; abelian integrals and differentials, separation of variables, integrable tops, FOS: Physical sciences, Relations of finite-dimensional Hamiltonian and Lagrangian systems with algebraic geometry, complex analysis, special functions, Mathematical Physics (math-ph), Dynamical Systems (math.DS), Hamilton-Jacobi equation, action function, Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics, Integrable cases of motion in rigid body dynamics, FOS: Mathematics, Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions, Relationships between algebraic curves and integrable systems, Mathematics - Dynamical Systems, Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics
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