Kovacic算法在Hess情形下重刚体定点运动研究中的应用
Application of the Kovacic algorithm for the investigation of motion of a heavy rigid body with a fixed point in the Hess case
摘要：
1890年，德国数学家和物理学家W.赫斯发现了新的特殊情况下可积的欧拉-泊松方程的运动的一个沉重的刚体与一个固定点。在1892年宾夕法尼亚州。涅克拉索夫证明，解决问题的运动沉重的刚体与一个固定点下赫斯条件减少到整合二阶线性微分方程。本文导出了相应的线性微分方程，并给出了其系数的有理形式。利用Kovacic算法证明了相应的二阶线性微分方程的Liouvillian解仅在运动刚体为Lagrange顶或面积积分常数为零的情况下存在。
英文摘要：
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.
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