中国空间科学技术

中国空间科学技术 ›› 2025, Vol. 45 ›› Issue (2): 70-78.doi: 10.16708/j.cnki.1000-758X.2025.0024

• 论文 • 上一篇    下一篇

柔性航天器动力学方程一般形式的工程简化方法

邹元杰*，邓润然，史纪鑫，葛东明   

  1. 北京空间飞行器总体设计部，北京100094
  • 收稿日期:2023-10-13 修回日期:2024-01-18 录用日期:2024-01-25 发布日期:2025-03-13 出版日期:2025-04-01

Engineering simplified approach to the general formulation for the dynamics of flexible spacecraft

ZOU Yuanjie*， DENG Runran， SHI Jixin， GE Dongming   

  1. Beijing Institute of Spacecraft System Engineering， Beijing 100094， China
  • Received:2023-10-13 Revision received:2024-01-18 Accepted:2024-01-25 Online:2025-03-13 Published:2025-04-01

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摘要： 在完备的柔性航天器动力学二阶微分方程一般形式的基础上，提出一般方程的工程简化方法。首先，采用平动集中质量方法对相关积分项进行了简化处理，忽略单元自身转动惯量对总惯量的影响以及板壳单元、梁单元等转角运动的影响，将体积分运算统一转化为节点相关变量与平动质量乘积的求和运算；其次，依据“小变形假设”，对含结构变形参量的方程系数矩阵进行简化，忽略结构振动位移对节点位置矢量的影响，使非线性系数矩阵转化为常系数矩阵。通过简化处理，柔性航天器动力学方程一般形式的所有项均被保留，而其积分项和系数矩阵的计算，在满足工程精度要求的前提下得到大幅简化，便于编程实现和工程实施。提出的工程简化方法主要用于柔性航天器在大范围、复杂运动过程中的动力学仿真分析，后续可以由单体动力学进一步拓展至多体动力学，解决在轨组装航天器、空间机器人/机械臂等空间结构系统的柔性多体动力学问题。数值算例验证了工程简化方法的合理性和有效性。

关键词: 柔性航天器, 动力学, 一般形式, 工程简化方法, 平动集中质量方法

Abstract: An engineering simplified approach to the general formulation for the dynamics of flexible spacecraft is presented on the basis of the complete second-order differential equations. First, the integral items are simplified based on the translational lumped mass method, and the element inertia and rotational motions for shell element or beam element are omitted. Thus, the complex volume integral computation is transformed to the summation operation of variables multiplied by translational masses. Second, the nonlinear matrix coefficients are simplified to constant matrix based on “the small deformation assumption”, while omitting the impact of the elastic displacements on the position vectors. Therefore, all the items of the general formulation for the dynamics of flexible spacecraft are well preserved, but their computation is remarkably simplified. The approach could be used for the analysis of flexible spacecraft with largeamplitude and complex motions, and further extended from single-body to multi-body in order to solve the dynamics of on-orbit construction structures or space robots/arms. Finally, the approach is verified by multiple numerical examples and an application case.

Key words: flexible spacecraft, dynamics, general formulation, engineering simplified approach, translational lumped mass method