3D刚体摆姿态平衡流形的稳定性研究  

Stability study on equilibrium manifold of 3D rigid pendulum

作　　者：张健丽[1] 戈新生[2] 

机构地区：[1]北京信息科技大学自动化学院,北京100192 [2]北京信息科技大学机电工程学院,北京100192

出　　处：《北京信息科技大学学报（自然科学版）》2014年第1期31-36,共6页Journal of Beijing Information Science and Technology University

基　　金：国家自然科学基金资助项目(11072038);北京市自然科学基金重点项目资助B类(KZ201110772039)

摘　　要：针对3自由度(3D,3-Degrees)刚体摆姿态平衡流形的稳定性问题进行了研究。利用3-2-1欧拉姿态角的描述方式建立了3D刚体摆的姿态动力学方程和运动学方程,并对其数学模型进行了姿态约化;由3D刚体摆的约化方程解得了4组彼此不相交的一维平衡流形,对3D刚体摆的姿态平衡流形进行了讨论,并绘出其在球面的平衡流形图,利用李亚普诺夫一次近似理论讨论了这4组平衡流形的稳定性,得出结论:3D刚体摆一维平衡流形为李亚普诺夫意义下不稳定,计算机仿真验证了这一结论。The stability of equilibrium manifolds of the three degrees of freedom （3D） rigid pendulum is studied in this paper. Using 3-2-1 Euler angles methods to build attitude dynamics and kinematics equations of 3D rigid pendulum,then reduced the completed equations. The one-dimensional equilibrium manifold is a solution of reduced equation of 3D rigid pendulum, which has four mutually disjoint groups. Equilibrium manifolds of 3D rigid pendulum are discussed. Then the equilibrium manifolds map is drawn in a spherical surface. Lyapunov approximation theory is used to discuss the stability of these four groups of equilibrium manifolds. It is concluded that the one-dimensional equilibrium manifold of 3 D rigid pendulum is unstable in the sence of Lyapunov, which is verified by a computer simulation.

关 键 词：3D刚体摆 平衡流形 李亚普诺夫一次近似理论 稳定性 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]