Structure-Preserving Analysis of Skeleton Structure of Solar Sail in the Deploying Process

太阳帆骨架简化模型自旋展开过程中保结构特性研究

School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an 710072, China

Received: 13 April 2017

Abstract

For the simplified dynamic model of the skeleton structure of solar sail in the solar power satellite via arbitrarily large phased array system (SPS-ALPHA) in the deploying process, the symplectic method is employed to simulate the dynamic behaviors of the skeleton structure of solar sail and the characteristic of vibration, the constraints default as well as the energy-preserving of the system are all discussed in this paper.Firstly, the simplified dynamic model of the skeleton structure is established based on the variational principle, which is rewritten in the form of the associated canonical equation in Hamilton framework from the Lagrange equation that describes the deploying process of the skeleton structure of solar sail. And then, the equation is numerically simulated by the symplectic Runge-Kutta method and the classical Runge-Kutta method respectively. Comparing with the classical Runge-Kutta method, the symplectic Runge-Kutta method employed in this paper can preserve the displacement constraint and the system energy well with excellent numerical stability.

摘要

针对相控阵空间太阳能电站系统（solar power satellite via arbitrarily large phased array，简称SPS-ALPHA）中太阳帆骨架自旋展开过程中的简化动力学模型，采用辛算法研究了太阳帆骨架的动力响应，并模拟分析了结构振动特性、约束违约及能量保持的情况。首先，建立太阳帆骨架展开过程中的简化模型，基于变分原理将描述简化模型的拉格朗日（Lagrange）方程导入哈密尔顿体系，进而建立模型的正则控制方程；随后，分别采用辛Runge-Kutta方法和经典Runge-Kutta方法模拟骨架结构自旋展开过程，并对比分析了展开过程中的位移约束及能量误差问题。数值模拟结果显示：与经典Runge-Kutta方法相比，辛Runge-Kutta方法能更好地处理骨架结构自旋展开过程中的约束违约问题及保持系统的总能量不变，并且具有良好的数值稳定性。