绳系空间太阳能电站动力学响应分析

Analysis of Dynamic Response of Tethered Space Solar Power Station

利用绝对节点坐标方法研究绳系空间太阳能电站在轨飞行的太阳能电池板动力响应。通过勒让德变换引入广义动量,在约束哈密尔顿体系下建立轨道、姿态和弹性振动耦合的动力学方程。基于祖冲之类方法的思想,结合辛龙格-库塔方法对微分-代数方程进行数值求解。数值算例说明本文建模方法和数值算法都是有效的,能很好地保持系统约束和能量。最后分析了绳长、平台系统的质量、轨道高度对于梁中点挠度和轴向平均应变的影响。

A procedure is proposed to establish the dynamical model and analyze the dynamic behaviors of a tethered space solar power station. The solar panels are modeled by the use of absolute nodal coordinate formulation with tight tethered constraints. The constrained Hamiltonian equations of coupled orbital motion, attitude motion and structural vibration are derived by using Legendre transformation and introducing generalized momenta. Based on the Zu Chong-zhi method, the Symplectic Runge-Kutta method is adopted to solve the differential-algebraic equations. Through a numerical experiment, the proposed method and model are verified, which reveals that the constraints and energy of the system are well preserved throughout the simulation. The effects of the tether length, bus mass and orbital altitude on the dynamic behaviors of the tethered space solar power station are finally discussed.