柔性多体航天器动力学

DYNAMICS OF FLEXIBLE MULTIBODY SPACECRAFTS

本文以柔性多体航天器为背景,用Jourdain变分原理建立一类无根树形柔性多体系统动力学通用模型。用独立的铰相对坐标描述相邻物体间的大位移运动,一致质量有限元法对变形体进行离散,并用通过振动正则模态变换引入的模态坐标描述物体的弹性小变形,得到一组由系统的轨道动力学方程,姿态动力学方程及系统振动方程组成的耦合形式的动力学微分方程组。由于采用通路矩阵、关联矩阵、瞬时增广体等概念,其形式与多刚体系统动力学方程兼容。文末对含中心刚体的二体及三体简单航天器模型进行动力学数值仿真。

On the background of flexible multibody spacecrafts, the general dynamic equations of motion of flexible multibody systems with nonrooted tree topologies are obtained by using Jouradin's principle. The large displacements between contigous bodies are described through independent relative joint coordinates, and the small deformation of bodies through modal coordinates from consistent mass finite element method and vibrational normal modal analysis. The result is a set of coupled dynamic equations consisting of orbital dynamic equations, attitude dynamic equations and vibrational equations. It is compatible with equations of rigid multibody systems because of using the concepts, such as path matrix, incidence matrix, instantaneous augmented body. Findlly, the simulation results of two bodies and three bodies simple spacecrafts including a main rigid body are presented.