一类多刚体中的混沌现象研究

Study on chaos in multi-body system

描述了一个圆盘对称连接各两个刚杆这样一个五自由度多刚体系统的模型,使用拉格朗日法建立了该系统的动力学方程,对动力学方程进行了仿真计算和分析.通过大量参数的变化运算后,将其中的一些物理参数和状态参数固定,只改变中心体圆盘的初始速度,利用相图、轨迹图、自相关和功率谱图作为判断依据,对仿真结果加以分析,确定此多刚体系统在各杆的初始位置为垂直向下处于静止状态、各样的初始速度为零、圆盘的初始速度为0.2-2.6m/s时,存在混沌现象.

A circular plate with 2 symmetrically linked staffs is described by a model of five degrees of freedom multi - body system. And the nonlinear dynamics equation of the system is established through Lagrange method. In the process of simulation, all physic parameters and the initial conditions are regulated except the initial velocity of the plate. According to the plots of the state track, phase plots, auto - correlation and the power -spectrum of staffs, it is determined that there are chaos phenomena in the model when the staffs are stationary in their vertical down initial positions, the initial velocities of the staffs are zero, and the initial velocity of the plate is 0.2-2.6.