具有刚性约束的非线性动力系统的局部映射方法

THE LOCAL MAP METHOD FOR NON-SMOOTH DYNAMICAL SYSTEMS WITH RIGID CONSTRAINTS

对具有刚性约束的n维非线性动力系统进行研究,建立了该类系统在刚性约束附近的局部映射关系.又根据连续性和横截性条件,通过几何方法推导并证明了局部映射的Jacobi矩阵的解析式.然后,通过引入局部映射,并利用Poincar啨映射方法,基于Floquet理论对刚性约束的n维非线性动力系统的周期运动的稳定性和分岔进行分析,给出了该类系统Poincar啨映射的Jacobi矩阵的计算方法.最后,以一类刚性约束的非线性动力系统为例,揭示了局部映射在其动力学分析中的重要作用.

A local map is presented for n-dimensional nonlinear dynamical systems with rigid constraints. The analytical formula of the Jacobian matrix of local map is obtained and proven by geometrical method according to the continuity and transversality condition. By introducing the local map and using the method of Poincaré map, the dynamical analysis of n-dimensional nonlinear dynamical systems with rigid constraints is made by means of the Floquet theory. The calculation method of the Jacobian matrix of Poincaré map is given. Finally, an important role of local map is shown in the dynamical analysis of a given nonlinear dynamical system with rigid constraints.