有干摩擦的倒立摆的不落运动
On motions without falling of an inverted pendulum with dry friction
摘要：
研究了一个支点水平移动的平面倒立摆。假定支点的运动规律已给定，摆在存在干摩擦的情况下运动。给出了摆不落在水平位置以下解存在的充分条件。证明是基于相应的微分包含的解是右唯一的且连续依赖于初始条件的事实，文中也证明了这一点。
英文摘要：
An inverted planar pendulum with horizontally moving pivot point is considered. It is assumed that the law of motion of the pivot point is given and the pendulum is moving in the presence of dry friction. Sufficient conditions for the existence of solutions along which the pendulum never falls below the horizontal positions are presented. The proof is based on the fact that solutions of the corresponding differential inclusion are right-unique and continuously depend on initial conditions, which is also shown in the paper.
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。
