一类非线性相对转动周期系统的平衡稳定性分析

利用一类周期性变系数线性常微分方程解的基本矩阵的Jordan形，分析一类非线性相对转动系统扭转的运动稳定性，从而得到非线性相对转动周期系统的运动稳定准则. 运用Lyapunov函数法，对广泛存在的一类机械传动系统的相对转动运动的平衡稳定位置的稳定域进行研究，并给出数学解析表达式. 这为工程中广泛存在的这类机械传动系统稳定工作区间工作参数的选取和相似模拟提供了理论依据及方法，据此可进一步分析和评价大型复杂旋转机械主传动系统的扭振稳定性. 关键词：相对转动相似模拟运动稳定平衡稳定

Analysis of stability of the equilibrium state of periodic motion in a nonlinear relative-rotation system

For solving stability of motion in a nonlinear relative rotation shafting, a sort of periodic variable coefficient linear ordinary differential equations was studied. Movement stabilization criterion of nonlinear relative rotation system was obtained by transferring the fundamental matrix of the solution of the ordinary differential equation to Jordan canonical. Using the Lyapunov function method, the stabile balance position of relative rotation motion of driving system in a variety of mechanical equipments was studied, and the analytic expression of the stable region was obtained. The method supplies theoretical laws, similarity analog criterion and technique means of selecting working parameter of stable working interval of a type of mechanical driving systems. The result of the research can be used for analysis and evaluation of the torsional vibration stability of the main driving system of heavy and complex rotary machines.