Existance of Liouvillian solutions in the problem of motion of a heavy rigid body with a fixed point under the action of gyroscopic forces in the Hess case

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The paper studies the problem of motion of a rigid body about a fixed point under the action of gravity and gyroscopic forces in the Hess integrability case. It is shown, that the solution of the problem is reduced to the integration of the second – order linear differential equation with rational coefficients. Using the Kovacic algorithm, we obtain the conditions on the parameters of the problem under which we can find the general solution of the corresponding second order linear differential equation in explicit form. It is also shown that in the case when the rigid body with a fixed point moves under the action of only gyroscopic forces, the general solution of the corresponding linear differential equation can be found in explicit form for any values of parameters of the problem.

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作者简介

A. Kuleshov

Lomonosov Moscow State University

编辑信件的主要联系方式.
Email: kuleshov@mech.math.msu.su
俄罗斯联邦, Moscow

A. Skripkin

Lomonosov Moscow State University

Email: alexander.kuleshov@math.msu.ru
俄罗斯联邦, Moscow

参考

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