Abstract

In mechanical autonomous conservative systems that admit a partial integral, there are sometimes stationary motions that exist both with and without a partial integral. A system is considered in which the Hess integral exists when the Appelroth equality is satisfied and the stationary motion is distinguished, which takes place even without the Appelroth equality. In the article, the stability of such a stationary motion is studied by the second Lyapunov method. It is found that the boundary of the region of sufficient stability conditions does not coincide with the boundary of the region of necessary stability conditions.

中文翻译：

---

Appelroth 等式的邻域中的一个永久旋转的稳定性

摘要

在允许偏积分的机械自治保守系统中，有时存在有和没有偏积分的静止运动。当满足 Appelroth 等式并区分静止运动时，考虑其中存在 Hess 积分的系统，即使没有 Appelroth 等式也会发生静止运动。文中用第二李雅普诺夫方法研究了这种静止运动的稳定性。发现充分稳定条件区域的边界与必要稳定条件区域的边界不一致。