| 3D刚体摆姿态平衡流形的稳定性研究 |
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| 引用本文： | 张健丽,戈新生.3D刚体摆姿态平衡流形的稳定性研究[J].北京机械工业学院学报,2014(1):31-36. |
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| 作者姓名： | 张健丽 戈新生 |
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| 作者单位： | [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 |
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| 基金项目： | 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） |
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| 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。
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| 关 键 词： | D刚体摆 平衡流形 李亚普诺夫一次近似理论 稳定性 |
Stability study on equilibrium .manifold of 3D rigid pendulum |
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| ZHANG Jian-li,GE Xin-sheng.Stability study on equilibrium .manifold of 3D rigid pendulum[J].Journal of Beijing Institute of Machinery,2014(1):31-36. |
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| Authors: | ZHANG Jian-li GE Xin-sheng |
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| Affiliation: | 1. Department of Automation, Beijing Information Science and Technology University, Beijing 100192, China; 2. Mechanical ＆ Electroical Engineering School, Beijing Information Science and Technology University, Beijing 100192, China) |
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| Abstract: | 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. |
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| Keywords: | 3 D rigid pendulum equilibrium manifold Lyapunov approximation theory stability |
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