Semianalytical solutions of relative motions with applications to periodic orbits about a nominal circular orbit
type: Item
instance of: scholarly article
title: Semianalytical solutions of relative motions with applications to periodic orbits about a nominal circular orbit
zbMATH Open document ID: 1427.70058
DOI: 10.1155/2018/4183941
author: Qiwei Guo
author: Hanlun Lei
author: Bo Xu
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: In the dynamical model of relative motion with circular reference orbit, the equilibrium points are distributed on the circle where the leader spacecraft is located. In this work, analytical solutions of periodic configurations around an arbitrary equilibrium point are constructed by taking Lindstedt-Poincaré (L-P) and polynomial expansion methods. Based on L-P approach, periodic motions are expanded as formal series of in-plane and out-of-plane amplitudes. According to the method of polynomial expansions, a pair of modal coordinates is chosen, and the remaining state variables are expressed as polynomial series about the modal coordinates. In order to check the validity of series solutions constructed, the practical convergence is evaluated. Considering the fact that relative motion model is a special case of restricted three-body problem, the periodic configurations constructed in the model of relative motion are taken as starting solutions to numerically identify the periodic orbits in restricted three-body problem by means of continuation technique with the mass of system as continuation parameter.
Mathematics Subject Classification ID: 70M20
Mathematics Subject Classification ID: 34A45
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 7018931
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/4183941
OpenAlex ID: W2834797179
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Wikidata QID: Q129565101
description: scientific article; zbMATH DE number 7018931