刚体定点惯性运动问题中约化系统的积分流形
Integral manifolds of the reduced system in the problem of inertial motion of a rigid body about a fixed point
摘要：
根据莫佩屠斯原理，在具有固定点的刚体的惯性运动问题（欧拉情形）中的简化系统等价于2-球面上的测地线流。我们描述了这种情况下的相拓扑结构，包括积分环的分叉类型。我们建立了奇异积分曲面的拓扑。利用$SO(3)$作为3-球的几何解释，确定了边界球的对点，我们证明了奇异积分曲面和2-环面族是如何在等能级上解决的，用当代的语言，可以说这是第一次描述$C_2$（$2T^2 \to 2T^2$）型的分支。
英文摘要：
The reduced system in the problem of the inertial motion of a rigid body with a fixed point (the Euler case) is equivalent, by the Maupertuis principle, to some geodesic flow on the 2-sphere. We describe the phase topology of this case including the types of the bifurcations of the integral tori. We establish the topology of the singular integral surfaces. Using the geometrical interpretation of $SO(3)$ as a 3-ball with opposite points of the boundary sphere identified we show how the singular integral surfaces and the families of 2-tori are settled in an iso-energy level.Using the contemporary language, one can say that this is the first description of the bifurcation of the type $C_2$ ($2T^2 \to 2T^2$).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
