{"title":"Exploring the equilibrium dynamics of an infinitesimal body in the perturbed problem of five bodies","authors":"Md Sanam Suraj, Elbaz I. Abouelmagd, Mani Bhushan, Md Chand Asique","doi":"10.1016/j.chaos.2024.115873","DOIUrl":null,"url":null,"abstract":"This work aims to analyze the dynamics of the restricted five-body problem when the primaries are non-spherical spheroids. We explored numerically three different scenarios: (i) when only the main body creates a potential with either oblateness or prolateness effect; (ii) when only peripheral bodies generate potentials with either oblateness or prolateness effects; and (iii) when all the primary bodies create potentials with either oblateness or prolate effects. We conducted a numerical analysis to study the motion of infinitesimal body under the gravitational influence of four non-spherical primaries. In this analysis, we revealed that the oblate or prolate bodies significantly affect the dynamics of the equilibrium points (EPs), their linear stability, and permissible regions of motion. Furthermore, we demonstrate that the total number of EPs depends on the mass parameter, the oblateness and prolateness parameters or the combinations of these parameters. The specific ranges of oblateness or prolateness values where the equilibrium points are linearly stable are also found.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"104 1","pages":""},"PeriodicalIF":5.3000,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos Solitons & Fractals","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1016/j.chaos.2024.115873","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
摘要
这项研究旨在分析当基体为非球形时受限五体问题的动力学。我们在数值上探索了三种不同情况:(i)当只有主体产生具有扁球形或扁球形效应的势时;(ii)当只有外围体产生具有扁球形或扁球形效应的势时;以及(iii)当所有主体产生具有扁球形或扁球形效应的势时。我们进行了数值分析,研究了无穷小体在四个非球形主天体引力影响下的运动。在分析中,我们发现扁球体或长球体会显著影响平衡点(EP)的动力学、其线性稳定性和允许的运动区域。此外,我们还证明了 EP 的总数取决于质量参数、扁圆度和扁长度参数或这些参数的组合。我们还找到了平衡点线性稳定的扁平率或扁平率值的具体范围。
Exploring the equilibrium dynamics of an infinitesimal body in the perturbed problem of five bodies
This work aims to analyze the dynamics of the restricted five-body problem when the primaries are non-spherical spheroids. We explored numerically three different scenarios: (i) when only the main body creates a potential with either oblateness or prolateness effect; (ii) when only peripheral bodies generate potentials with either oblateness or prolateness effects; and (iii) when all the primary bodies create potentials with either oblateness or prolate effects. We conducted a numerical analysis to study the motion of infinitesimal body under the gravitational influence of four non-spherical primaries. In this analysis, we revealed that the oblate or prolate bodies significantly affect the dynamics of the equilibrium points (EPs), their linear stability, and permissible regions of motion. Furthermore, we demonstrate that the total number of EPs depends on the mass parameter, the oblateness and prolateness parameters or the combinations of these parameters. The specific ranges of oblateness or prolateness values where the equilibrium points are linearly stable are also found.
期刊介绍:
Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.