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Эта публикация цитируется в 5 научных статьях (всего в 5 статьях)
Separation of Variables and Explicit Theta-function Solution of the Classical Steklov–Lyapunov Systems: A Geometric and Algebraic Geometric Background
Yuri Fedorov, Inna Basak Department de Matemática Aplicada I,
Universitat Politecnica de Catalunya,
Barcelona, E-08028 Spain
Аннотация:
The paper revises the explicit integration of the classical Steklov–Lyapunov systems via separation of variables, which had been first made by F. Kötter in 1900, but was not well understood until recently. We give a geometric interpretation of the separating variables and then, applying the Weierstrass hyperelliptic root functions, obtain explicit theta-function solution to the problem. We also analyze the structure of poles of the solution on the Jacobian on the corresponding hyperelliptic curve. This enables us to obtain a solution for an alternative set of phase variables of the systems that has a specific compact form.
In conclusion we discuss the problem of integration of the Rubanovsky gyroscopic generalizations of the above systems.
Ключевые слова:
Steklov–Lyapunov system, explicit solution, separation of variables, algebraic integrability.
Поступила в редакцию: 30.06.2010 Принята в печать: 26.08.2010
Образец цитирования:
Yuri Fedorov, Inna Basak, “Separation of Variables and Explicit Theta-function Solution of the Classical Steklov–Lyapunov Systems: A Geometric and Algebraic Geometric Background”, Regul. Chaotic Dyn., 16:3-4 (2011), 374–395
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd443 https://www.mathnet.ru/rus/rcd/v16/i3/p374
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