随机Chaplygin系统平衡状态流形的矩不稳定性

目的 研究Ｃｈａｐｌｙｇｉｎ系统平衡状态流形在随机扰动下的不稳定性。方法 首先，建立随机Ｃｈａｐｌｙｇｉｎ系统的运动微分方程；其次，给出与扰动方程对应的一次矩和二次矩方程并将其线性化；最后，利用Ｌｉａｐｕｎｏｖ第一近似理论，判断系统的矩不稳定性。结果与结论 给出判断随机Ｃｈａｐｌｙｇｉｎ系统不稳定性的判据，并举例说明其应用。

Moment Unstability of Stochastic Chaplygin System's Equilibrium State Manifold

Aim To study the unstability of Chaplygin system's equilibrium state manifold under the random perturbation. Methods Firstly, the stochastic differential equations of Chaplygin system was established; then, the first and second linearization moment equations corresponding to the system were given, at last, the moment unstability of the stochastic system according to the theory of Liapunov was judged. Results and Conclusion The criterion for juaging the unstability of stochastic Chaplygin system was obtained and one example was given to illustrate the application of the criterion.