航天器相对运动建模及周期性相对运动求解

面向航天器编队飞行的需求,对椭圆参考轨道航天器非线性周期相对运动条件进行研究,提出了确定椭圆参考轨道编队航天器非线性周期性相对运动条件的新方法。首先,考虑非线性、椭圆轨道等因素,通过哈密尔顿-雅可比(HJ)方程和正则摄动理论,推导了在任意非线性摄动下相对运动的模型和获得不需消耗任何燃料的周期性相对运动轨道的条件;然后,采用时域配点法,结合改进的列文伯格-马夸尔特(LM)法对周期性相对运动的初值进行求解;最后,设计数值仿真算例,利用上述条件,得到不消耗任何燃料的周期性绕飞轨道,由此验证了本文所提模型和方法的正确性。

Spacecraft Relative Motion Modeling and Periodic Motion Solving

For the requirements in the spacecraft formation flying mission, a new method considering the effects of nonlinearity and eccentricity is proposed to design periodic relative rotating orbits. Considering reference orbit eccentricity and nonlinear relative motion,the model of relative motion in any perturbation and conditions of invariant periodic relative rotating orbit are derived with Hamiltonian-Jacobi equations and the canonical perturbation theory. Then,the initial condition for the periodic relative rotating orbit is obtained by the time domain collocation method and the Levenberg-Marquardt(LM) method. Finally,several numerical simulation examples are designed to verify the effectiveness of the model and the methodology. It is shown that the periodic relative rotating orbit without consuming any fuel can be found by using these conditions.