具有积极约束的Lagrange系统的能控性
On the Controllability of Lagrangian Systems by Active Constraints
摘要：
我们考虑一个机械系统，这是通过移动约束控制。也就是说，我们假设一些坐标可以直接指定为时间的函数，通过无摩擦约束。这导致了一个系统的常微分方程的右手边二次依赖于时间的控制导数。本文引入了一个简化的动力学模型，它用一个微分包含来描述.我们证明了，每一个轨迹的微分包含可以一致地近似的轨迹的原始系统，在一个足够大的时间间隔，开始在休息。在一个更强的假设下，我们证明了第二条轨迹到达完全相同的终点。
英文摘要：
We consider a mechanical system which is controlled by means of moving constraints. Namely, we assume that some of the coordinates can be directly assigned as functions of time by means of frictionless constraints. This leads to a system of ODE's whose right hand side depends quadratically on the time derivative of the control. In this paper we introduce a simplified dynamics, described by a differential inclusion. We prove that every trajectory of the differential inclusion can be uniformly approximated by a trajectory of the original system, on a sufficiently large time interval, starting at rest. Under a somewhat stronger assumption, we show this second trajectory reaches exactly the same terminal point.
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。
