树型刚柔机械多体系统递推动力学与广义―α求解算法

A generalized-αtime integration and recursive dynamics method for tree rigid-flexible multibody system

研究树型柔性航天器动力学高效率建模和高精度广义―α的数值求解算法。利用拓扑结构和连接矩阵的方法描述树型机械多体系统,采用图论的方法将树型系统分解为多条链式系统;对系统中铰的驱动情况分别定义为主动铰和被动铰,通过铰链的类型以及判断是刚性体或者柔性体,基于空间算子代数理论建立树型系统的动力学模型;采用广义―α算法求解加速度约束的动力学微分—代数方程组。最后通过软件编制仿真验证本研究内容的正确性和高效性。

Generalized efficient recursive dynamics model of a kind of flexible spacecraft with appendages system was built.The flexible spacecraft system was described by the topology method and the lower body array.The method of describing the under-actuated rigid-flexible multibody system based on Spatial Operator Algebra（SOA）theory was proposed.The generalized flexible spacecraft was described in according to the type of the joint（active or passive）,and the rigid body or the flexible body;then the generalized articulated inertia-matrix,the residual forces and the generalized acceleration and torque were computed through twice tip-to-base recursive and once base-to-tip recursive;the generalized torque and the acceleration was linear added at the branch,at last generalized-αmethod is presented for stiff dynamic equations of multibody systems based on the constraints projection method.Simulations results show that the dynamic modeling and fast integration techniques proposed in this paper are very useful.