可折叠航天结构展开动力学分析

以欧拉参数为广义坐标（准坐标），相对角速度和相对移动速度为广义速率，采用Ｋａｎｅ方程的Ｈｕｓｔｏｎ形式建立多体系统的运动力学方程。由伪上三角分解求约束Ｊａｃｏｂｉ矩阵的正交补阵，约简约束力，从而将运动方程由微分几何方程（ＤＡＥ）变为常微分方程（ＯＤＥ），并由Ｇｅａｒ法对ＯＤＥ积分求出运动历程。最后给出一伸展臂数值分析算例。

Dynamic analysis for deployment process of foldable aerospace structures

Based on Huston's form of Kane's equation, equations of motion are formulated for deployable/retractable aerospace structures, with recursive Euler parameter and translation supposed as generalized coordinate, and recursive angular velocity and translation velocity as generalized velocity. The orthogonal complement to constrained Jacobi B is developed through pseudo uppertriangular depomposition (PUTD) method, based on Householder transformation, and Gramn\|Schmidt orthogonal process. Differential algebraic equations(DAEs) are reduced to ordinary differential equations(ODEs) with elimination of undetermined multipliers using PUTD. Time history of motion is got through Gear's integration algorithm. Numerical example proves that the foreging algorithm is suitable for deployment analysis of deployable aerospace structures.