含轴对称太阳翼的航天器耦合动力学

Coupling Dynamics of Spacecraft with Axisymmetric Solar Wings

摘要: 随着航天领域的快速发展，现如今的航天器主刚体平台上往往安装有大尺寸的柔性附件，由于柔性附件与航天器主刚体的耦合效应，会对航天器的运动轨迹以及姿态产生大的影响。精确有效的航天器动力学模型是进行刚柔耦合效应研究的基础。本文主要研究了含轴对称太阳翼柔性航天器的耦合动力学模型，将太阳翼等效为Euler-Bernoulli梁模型，采用Euler-Bernoulli梁的内力平衡关系以及牛顿第二定律得到梁的振动微分方程，从而建立航天器柔性附件的动力学模型，采用假设模态法和分离变量法对柔性附件动力学方程进行求解。利用准坐标下的拉格朗日方程和牛顿第二定律，得到航天器刚体平台和柔性附件振动的耦合动力学方程。并通过MATLAB进行数值仿真，仿真结果表明：当柔性航天器受到零脉冲外力和外力力矩的作用时，其位置和角度都会发生变化。当外力和外力矩为零时，由于刚–柔性耦合效应，航天器的速度和角速度不收敛到零；航天器柔性附件的最大振动振幅与小变形的假设相一致；航天器的两个柔性附件在外力和力矩的作用下所表现出的端部位移是对称的，表现出相同的振幅和相反的位移。当外力和力矩为零后，航天器的柔性附件仍存在残余振动。该研究为后续航天器姿态控制器的设计提供前提条件。

Abstract: The main rigid body platform of modern spacecraft is often equipped with large-size flexible attachments due to the rapid development of the aerospace engineering. The coupling effect between the flexible attachments and the main rigid body of the spacecraft will have great influence on the trajectory and attitude of the spacecraft. The precise and effective spacecraft dynamics model is the basis for conducting the study of rigid-flexible coupling effects. In this paper, the coupled dynamics model of flexible spacecraft with axisymmetric solar wing is mainly studied, and the solar wing is modeled to Euler-Bernoulli beam model, and the internal force equilibrium relationship of Euler-Bernoulli beam and Newton’s second law are used to obtain the vibration equations of the beam, so as to establish the dynamics model of the spacecraft’s flexible attachments, and the hypothetical modal method and the method of separating variables are used to solve the dynamics equations of the flexible attachments. Using the Lagrange equation and Newton’s second law in quasi-coordinates, the coupled dynamic equations of the spacecraft rigid platform and flexible attachment vibration are obtained. Then the numerical simulation is carried out by MATLAB, and the simulation results show that: when the flexible spacecraft is subjected to zero impulse external force and external moment, its position and attitude are changed. When the external force and moment are zero, the velocity and angular velocity of the spacecraft do not converge to zero due to the stiff-flexible coupling effect; the maximum vibration amplitude of the flexible attachments of the spacecraft is consistent with the assumption of small deformation; and the end displacements of the two flexible attachments of the spacecraft under the action of the external force and moment are symmetric, showing the same amplitude and opposite displacements. When the external force and moment are zero, residual vibration still exists in the flexible attachments of the spacecraft. This study provides a prerequisite for the design of subsequent spacecraft attitude controllers.