{"title":"The behavior of a satellite trajectory near the equilibrium points of sun-earth system and its control","authors":"L. Shalby, Noha Ali","doi":"10.2298/tam220816003s","DOIUrl":null,"url":null,"abstract":"In this paper, the behavior of a satellite trajectory near the equilibrium points of the Sun-Earth system is studied. The equations describing the motion of the satellite in the circular restricted three body problem for the Sun-Earth system, are discussed for their ordinary differential equations form, and Lagrange points are determined. Then, the stability is studied at each Lagrange point. The trajectories of a satellite starting its motion near Lagrange points are illustrated, showing the stability and instability behavior. Finally, the unstable trajectory is controlled by using ??2-method at ??1 as an example.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Applied Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2298/tam220816003s","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
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Abstract
In this paper, the behavior of a satellite trajectory near the equilibrium points of the Sun-Earth system is studied. The equations describing the motion of the satellite in the circular restricted three body problem for the Sun-Earth system, are discussed for their ordinary differential equations form, and Lagrange points are determined. Then, the stability is studied at each Lagrange point. The trajectories of a satellite starting its motion near Lagrange points are illustrated, showing the stability and instability behavior. Finally, the unstable trajectory is controlled by using ??2-method at ??1 as an example.
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