简单力学系统的稳定性

The stability of simple mechanical systems

研究了简单力学系统的稳定性问题,利用李亚普诺夫方法证明了建立在欧氏空间上的简单力学系统的平衡点总是局部稳定的,同时利用李亚普诺夫方法和微分几何控制理论证明了建立在一般黎曼流形上的简单力学系统在满足某种条件下,平衡点是局部稳定的,但不是渐近稳定的.

The stability of simple mechanical systems is studied. It is proved that the equilibrium point of the simple mechanical systems on Euclidean space is stable by using Lyapunov method. At the same time, it is also proved that the equilibrium point of the simple mechanical systems on Riemannian manifold is stable but not asymptotically stable by using Lyapunov method and differential geometric control theory.