3D刚体摆非线性动力学姿态特性研究

研究了3D刚体摆在一般情况和轴对称情况下的姿态动力学特性。通过建立3D刚体摆的动力学方程和运动学方程,利用非线性动力学的方法讨论了轴对称和非轴对称3D刚体摆的姿态运动。通过对两种情形刚体摆模型悬垂平衡位置加小摄动考察其姿态运动,可以发现在非轴对称情况下3D刚体摆出现混沌运动,在轴对称3D刚体摆情况下出现概周期运动。利用MATLAB进行仿真实验,分别得出非轴对称3D刚体摆的混沌姿态运动曲线和轴对称3D刚体摆的姿态概周期运动曲线,并分别给出庞加莱截面图。

Attitude dynamics of nonlinear properties of 3D rigid pendulum

The attitude dynamics of 3D rigid body placed in the general case and axial symmetry is studied. Firstly, 3D rigid body dynamics equation and kinematics motion are established, and then non- axisymmetric and axisymmetrie 3D rigid body attitude motions are discussed by the method of nonlinear dynamics. Through analyzing attitude stabilities of the perturbed motions respectively corresponding to two equilibrium positions of the rigid body pendulum, it is found that 3D rigid pendulum can exhibit chaotic motion in non-axisymmetric case and quasi-periodic motion in axisymmetric case. Finally, through the simulation experiments by using MATLAB software, the attitude motion curves for non- axisymmetric 3D rigid pendulum and the quasi-periodic motion curves for axisymmetric 3D rigid pendulum are presented. The figures of Poineare section for both non-axisymmetric and axisymmetric cases are also shown.