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中文摘要：
利用离散变分的数值积分方法研究3D刚体摆（3 Dimensional rigid pendulum）的姿态动力学数值计算问题。针对3D刚体摆的运动学及动力学方程解的稳定性及其能量、角动量与范数进行了数值仿真。在离散变分方法中引入李群概念,首先对3D刚体摆模型的简化形式——球摆做数值求解,然后分别对3D刚体摆的悬垂及倒置两种特殊情况进行数值求解,并将其结果与4阶龙格-库塔方法求解的结果进行比较。从数值仿真实验中可以看出,离散变分的数值积分方法相比龙格-库塔方法具有更高的精度。由此可得出李群离散变分方法具有较好的保结构及保能量特性。
英文摘要：
The numerical method of attitude equation for 3D（3 Dimensional）rigid pendulum is studied in this paper with discrete variation method.The simulation diagram of energy,angular momentum and norm for 3D rigid pendulum is made with MATLAB.Firstly,the basic concept of Lie group is introduced into discrete variation method,and then the attitude equation of spherical pendulum is solved as an special model of 3D rigid pendulum with this method.Secondly,the solving method of their attitude equation is studied,and the result is compared with that of Runge-Kutta method.It is concluded that the discrete variation is a high-precision symplectic method.
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