Communications in Nonlinear Science and Numerical Simulation ( IF 3.9 ) Pub Date : 2020-12-15 , DOI: 10.1016/j.cnsns.2020.105668 Ayansola D. Ogundele , Olufemi A. Agboola , Subhash C. Sinha
The relative orbital motion problem of a deputy spacecraft with respect to a chief spacecraft is, generally, described using a set of differential equations governing the motion of the spacecraft relative to each other instead of describing their motion, separately, relative to the Earth. In this paper, new time-varying, time periodic cubic approximation model of spacecraft relative motion is developed from the original nonlinear relative equations of motion with the chief in elliptical orbit. Afterwards, averaging method is applied to the cubic model to obtain asymptotic approximations and periodic solutions. The formulation of the averaging solutions using averaging method affords us the opportunity to have a better insight of the relative motion dynamics. From the numerical simulations, the averaging model is in close agreement with the nonlinear model. This can be attributed to the inclusion of cubic nonlinear terms. The model is amenable to the long-term prediction of the behavior of the relative motion and useful for spacecraft formation flying analysis.
中文翻译:
非线性航天器交会与编队飞行问题的数学建模与平均方法
通常,使用控制航天器相对于彼此的运动的一组微分方程来描述副航天器相对于主要航天器的相对轨道运动问题,而不是分别描述其相对于地球的运动。本文从椭圆轨道上的主运动的原始非线性相对运动方程出发,建立了航天器相对运动的时变,时间周期三次近似模型。然后,将平均方法应用于三次模型以获得渐近逼近和周期解。使用平均方法制定平均解决方案,使我们有机会更好地了解相对运动动力学。从数值模拟来看 平均模型与非线性模型非常吻合。这可以归因于包含三次非线性项。该模型适用于相对运动行为的长期预测,可用于航天器编队飞行分析。