中文摘要：

研究一类高维相对转动非线性动力系统的降维与分岔特性．在考虑转动系统中间隙非线性影响因素的基础上，基于广义耗散系统拉格朗日原理，建立了一类高维相对转动非线性系统动力学模型．采用Lyapunov-Schmidt（LS）约化方法，通过对高维非线性动力系统进行降维处理，得到能够揭示系统非线性动力特性与系统参数之间规律的低维等价分岔方程．运用奇异性理论对分岔方程进行普适开折，分析了系统的分岔特性．结合实例参数，对分岔特性进行仿真分析，得到相对转动非线性动力系统发生动力失稳的参数区域及系统参数对动力失稳的影响规律．

英文摘要：

The dimensionality reduction and bifurcation of some high-dimensional relative-rotation nonlinear dynamical system are stud- ied. Considering the nonlinear influence factor of a relative-rotation nonlinear dynamic system, the high-dimensional relative-rotation torsional vibration global dynamical equation is established based on Lagrange equation. The equivalent low-dimensional bifurcation equation, which can reveal the low-dimensional equivalent bifurcation equation between the nonlinear dynamics and parameters, can be obtained by reducing the dimensionality system using the method of Lyapunov-Schmidt reduction. On this basis, the bifurcation characteristic is analyzed by taking universal unfolding on the bifurcation equation through using the singularity theory. The simulation is carded out with actual parameters. The parameter region of torsional vibration and the effect of the parameters on the vibration are discussed.