中文摘要：

针对非完整约束系统的高非线性和强耦合性导致整个系统存在着动力学特性复杂及运动稳定性难以分析等问题,通过空间算子代数方法建立系统的动力学模型,在此基础上采用李雅普诺夫指数方法分析了系统的运动稳定性,建立了动力学参数与系统稳定性之间的量化关系.最后以小车倒立摆为例,对整个算法的有效性进行验证.该方法与李雅普诺夫第二法相比,主要优点在于其可构建性,并能够量化分析系统动力学参数与运动稳定性之间的关系,可为机械结构设计及控制系统优化提供参考.

英文摘要：

The high nonlinear and strong coupling characteristics of nonholonomic constraint systems usually result in the complexity of dynamic characteristics and the difficulty of analyzing kinetic stabil-ity .Spatial operator algebra methods was used to structure a dynamical model .Based on this ,by using Lyapunov exponent method ,the kinetic stability of the system was analyzed and quantized rela-tion between the kinetic parameters and the stability of system was built .Ultimately ,the cart invert-ed pendulum was taken for example to verify the validity of the whole arithmetic .As compared to its counterpart of Lyapunov′s second method ,the main advantage of the concept of Lyapunov exponents is that the methods for calculating the exponents are constructive and allowing to analyze the relation between the kinetic parameters and the kinetic stability which provides a reference for the design of mechanical structure and the optimization of control system .