以大型空间绳系辅助返回系统为背景,利用微元法和拉格朗日方程建立有分布质量的柔性绳系辅助返回系统的展开动力学模型。针对模型复杂的非线性和强耦合问题,采用Galerkin法进行离散化处理以求解;引入经典的珠子模型,以验证Galerkin法解的准确性;最后通过数学仿真来验证和分析Galerkin法解的正确性和收敛性, 并对绳系辅助返回系统的展开动力学特性进行适当的分析。仿真结果表明:本文建立的柔性绳系辅助返回系统的展开动力学模型以及基于Galerkin法对动力学模型的求解是正确的,解法是收敛的。
Under the background of big tethered-assisted return system, the deployment dynamic model for mass-distributed flexible tethered-assisted return system is given based on the micro-element method and Lagrange equation. For the complicated nonlinear and strongly coupled dynamic model, the dynamic model is discretize to obtain numerical solution by Galerkin method, and the typical lumped mass model is introduced to validate the Galerkin method. Then a mathematical simulation is provided to validate the solution of the Galerkin method, and analyze the dynamic characteristics of the system. The result indicates that the model for mass-distributed flexible tethered-assisted return system given in this article is correct, and the solution obtained by Galerkin method is also accurate and convergent.
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