基于广义逆矩阵形态解析的含三维间隙动力学保总能量算法研究

Precision deployable spacecraft structures such as large aperture reflector antennas have plenty of three-dimensional pair clearances so that it leads to extremely high system degree and makes the deploying dynamic analysis difficult. Thus, it is urgently needed to develop the highly efficient and accuracy algorithm. For this reason, it is significant to study on the dissipated energy calculation caused by collision and friction in three-dimensional clearances and the total energy preserving calculation of the non-conservative multibody system. The deploying dynamics Generalized Inverse Matrix Morphological Analysis Method will be utilized as main theory because of its better applicability and efficiency. The three-dimensional pair Jacobian matrix will be modeled to obtain the generalized mechanism displacement modality by generalized inverse matrix and form the dynamic equations. The Lankarani-Nikravesh contact force model and the LuGre friction force model will be modified to derive the dissipated energy calculating formula caused by clearance collision and friction. The modified projection symplectic Runge-Kutta method will be proposed. The generalized momentum will be introduced to form Hamilton Canonical Equation and the sub-state modified total energy preserving algorithm considering the dissipated energy modifying coefficient. Furthermore, generalized multi-symplectic method will be derived to study the clearance dissipated energy. Finally, it will be formed to get the high precision total energy preserving algorithm for non-conservative multi-body system dynamics considering three-dimensional clearances. The typical complicated spacecraft deploying dynamic models will be analyzed to validate the effectiveness of this method, so as to provide theoretical methods and technical means for practical engineering applications.

精密可展开航天器结构如大口径反射面天线存在大量三维运动副间隙，造成系统的维数极高，制约展开动力学分析，急需发展能同时保持高效和高精度的计算方法。为此，关于多体系统三维间隙的碰撞摩擦耗散能量计算及非保守动力学系统保总能量算法的研究有重要的意义。本项目拟采用具有良好适用性和高效性的基于广义逆矩阵展开动力学形态解析方法作为基本理论，建立三维运动副约束雅可比矩阵模型，利用广义逆矩阵得到广义机构位移模态，形成动力学方程。修正L-N接触力模型和LuGre摩擦模型并推导间隙耗散能量公式。提出考虑能量耗散的改进投影辛R-K方法；引入广义动量形成哈密顿正则方程，提出分状态求解能量耗散修正系数的改进保总能量算法；进一步研究间隙能量耗散的广义多辛方法。最终形成含三维运动副间隙的非保守多体系统动力学高精度保总能量计算方法，对典型复杂航天器展开动力学模型验证本方法的有效性并为实际工程应用提供理论方法和技术手段。

本项目是基于广义逆矩阵形态解析的含三维间隙动力学保总能量算法研究。针对空间可展开航天器结构高精度展开成型分析的工程需求，对含三维运动副间隙模型的展开动力学高效高精度计算方法研究。基于约束雅可比矩阵零空间理论，采用基于广义逆矩阵展开动力学形态解析方法作为理论基础，提出了一种新的空间可展开柔性多体系统动力学高效率建模方法以分析含三维运动副间隙极高维数模型展开动力学特性。本研究具有良好的工程适用性、建模开放性和计算高效性，是技术手段的创新，提供了一种极高维数模型的建模分析方法，体现了多体动力学和结构工程的多学科交叉特色。将基于广义逆矩阵形态解析方法引入到哈密顿系统下，提出分状态求解能量耗散修正系数的改进保总能量算法，以适用于三维运动副间隙碰撞摩擦的非保守动力学系统保总能量的计算。本方法具有较高的计算精度和稳定性，是计算方法的难点攻克和创新。同时，本项目的研究以空间结构为主要对象和应用，上述研究成果，在航天大型复杂空间结构如可展开固面反射面天线等有了很好的应用，对于大型可展开结构的动力学分析与控制具有一定的理论指导意义和技术参考价值。本项目的研究拓展到各类极高维结构的动力学分析与控制领域，也有一定的应用前景。