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中文摘要：
3D刚体摆为一个刚体在重力、扰动和控制力或力矩的作用下绕一个固定、无摩擦的支点旋转，具有三个转动自由度的刚体摆模型．针对3D刚体摆姿态稳定的非线性控制设计问题，给出基于欧拉四元数描述的3D刚体摆的姿态运动方程，证明了系统满足无源性条件，构造了系统的Lyapunov函数，利用能量法设计出3D刚体摆的姿态控制律，并由LaSalle不变集原理证明了该控制律的渐近稳定性．仿真实验给出了3D刚体摆在悬垂平衡位置的姿态和角速度的渐近稳定性，仿真实验结果表明基于能量方法的3D刚体摆姿态控制是有效的．
英文摘要：
3D rigid pendulum is a rigid body connects with the fixed pivot and a rigid body with three rotational degrees of freedom pendulum model. The attitude kinematic equations for nonlinear control of attitude stabilization of 3D rigid pendulum based on the quatemion parameterization were proposed. It proved the system to meet the passive condition and design the system＇s Lyapunov function with the 3D rigid pendulum＇s attitude control law by using the energy method. The LaSalle invariant principle was used to prove the control law＇s asymptotic stability. The simulation results show that the attitude and angular velocity are asymptotic stability of the 3D rigid pendulum in the situation of hanging equilibrium and the simulation resutts verify the availability of the method.
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