本文讨论刚体动力学中关于欧拉—泊松方程组可积必要条件的两个定理,引用了一些简单的例子说明,定理中的多值函数可能与运动的分叉有关,而李亚普诺夫所采用的基于解中不出现多值的复对数的方法,没有力学意义。所以可积必要条件的研究仍然不能算完成。

Two Classical Theorems for Dynamics of Rigid Bodies Gu DeganIn this paper, we discuss the two theorems on. the necessary condition of integrability of Euler-Poisson's equations in the dynamics of a rigid body.Simple examples are introduced to show that the multivalued functions may be related with bifurcations in motion. Based on the absence of multivalued complex logarithmic function in the solutions the method used by Liapunov has no meanings in mechanics. Therefore, the study of necessary condition for integrability is unfinished yet.