空间刚性梁轨道与姿态耦合动力学问题的辛分析

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摘要以空间结构中某些大刚度小尺寸连接件在轨组装之前的动力学问题为研究背景，建立了空间刚性梁的轨道与姿态耦合问题的动力学模型。针对建立的保守动力学模型，采用辛龙格库塔方法模拟了刚性梁的动力学行为，从刚性梁的轨道半径、真近角和姿态角演化过程的数值结果中，发现了随着初始姿态角速度的增加，梁轨道与姿态之间的耦合效应将加剧；通过记录每一时间步的系统总能量相对误差，并与传统龙格库塔方法的计算结果进行对比，间接地验证了所得到数值结果的正确性，同时也验证了辛龙格库塔方法的长时间数值稳定性。

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	尹婷婷1
	邓子辰1
	2
	蒋宪宏1

关键词 ：刚性梁, 轨道与姿态耦合, 辛龙格库塔方法, 保能量

Abstract：Taking dynamic problems of some large stiffness and small size adapting pieces in complex spatial structures before on-orbit assembly as studying background, the orbit-attitude coupled dynamic model for spatial rigid beams was established. With this dynamic model, the symplectic Runge-Kutta method was adopted to simulate dynamic behaviors of a spatial rigid beam. From the obtained numerical results about evolution processes of the beam’s orbit radius, true anomaly and attitude angle, it was shown that with increase in initial attitude angular speed, the orbit-attitude coupled effects become more obvious; the relative error of the system total energy within each time step is recorded, all relative errors are compared with those in the numerical results using the classic Runge-Kutta method, the correctness of the numerical results using the symplectic Runge-Kutta method and the long-time numerical stability of the symplectic Runge-Kutta method are verified.

Key words： rigid beam orbit-attitude coupling symplectic Runge-Kutta method energy-preserving

收稿日期: 2017-05-05 出版日期: 2018-04-28

引用本文:

尹婷婷1，邓子辰1, 2，蒋宪宏1. 空间刚性梁轨道与姿态耦合动力学问题的辛分析[J]. 振动与冲击, 2018, 37(9): 168-172.
YIN Tingting1, DENG Zichen1,2, JIANG Xianhong1. Symplectic analysis for orbit-attitude coupled dynamic problem of spatial rigid beams. JOURNAL OF VIBRATION AND SHOCK, 2018, 37(9): 168-172.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2018/V37/I9/168

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