Existence of liouvillian solutions in the problem of motion of a heavy rigid body with a fixed point in the Hess case

Авторы: Kuleshov Alexander, Bardin Boris
Сборник: Regular and Chaotic Dynamics: In memory of Alexey V. Borisov: Book of Abstracts
Серия: ANS Conference Series
Тезисы
Год издания: 2021
Место издания: Institute of Computer Science Moscow - Izhevsk
Первая страница: 45
Последняя страница: 46
Аннотация: In 1890 German mathematician and physicist W. Hess found new special case of integrability of Euler – Poisson equations of motion of a heavy rigid body with a fixed point. In 1892 P. A. Nekrasov proved that thesolution of the problem of motion of a heavy rigid body with a fixed point under Hess conditions reduces to integrating the second order linear differential equation. To obtain this equation we firstly derive the Euler – Poisson equations in the special Kharlamov coordinate system. Using this formof the Euler – Poisson equations we derive the corresponding linear differential equation and transform its coefficients to the form of rational functions. Applying the Kovacic algorithm to the obtained differential equation, we proved that the liouvillian solutions of the corresponding second order linear differential equation exists only in the case, when the moving rigid body isthe Lagrange top, or in the case, when the constant of the area integral is zero.
Добавил в систему: Кулешов Александр Сергеевич

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