Mathematical modeling and simulation of nonlinear spacecraft rendezvous and formation flying problems via averaging method

• Published in: Communications in nonlinear science & numerical simulation 2021-04, Vol.95, p.105668, Article 105668
• Main Authors: Ogundele, Ayansola D., Agboola, Olufemi A., Sinha, Subhash C.
• Format: Article
• Language: English
• Subjects: Asymptotic methods; Averaging; Chief spacecraft; Clohessy–Wilshire (CW) equation; Deputy spacecraft; Differential equations; Elliptical orbits; Equations of motion; Formation flying; Mathematical models; Motion control; Nonlinear systems; Relative motion; Space rendezvous; Spacecraft; Tschauner–Hempel (TH) equation
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2020.105668

•Mathematical model of governing differential equations is presented.•Radial, along-track and cross-track slowly varying parameters are developed.•Averaging method is applied to the nonlinear equation of relative motion.•The averaged model is useful for rendezvous and formation flying control approaches. 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.