论文标题
毛ac算算法的应用用于调查hess案中具有固定点的重刚体运动的运动
Application of the Kovacic algorithm for the investigation of motion of a heavy rigid body with a fixed point in the Hess case
论文作者
论文摘要
1890年，德国数学家和物理学家W. Hess发现了Euler的整合性的新特殊案例 - 具有固定点的重型刚体的运动方程。 1892年，P。A。Nekrasov证明了在HESS条件下具有固定点的重刚体运动问题的解决方案减少了二阶线性微分方程。在本文中，得出相应的线性微分方程，其系数以有理形式呈现。使用Kovacic算法，我们证明了相应的二阶线性微分方程的Liouvillian解仅在移动刚体为Lagrange顶部或区域积分常数为零时才存在。
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 the solution 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. In this paper the corresponding linear differential equation is derived and its coefficients are presented in the rational form. Using the Kovacic algorithm, we proved that the liouvillian solutions of the corresponding second order linear differential equation exists only in the case, when the moving rigid body is the Lagrange top, or in the case when the constant of the area integral is zero.
