{"title":"具有不稳定拉长原基的扰动受限三体问题中的非共轭平衡点","authors":"Ravi Kumar Verma, Badam Singh Kushvah","doi":"10.1007/s12648-024-03383-1","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we have studied the motion around the non-collinear equilibrium points in the perturbed circular restricted three-body problem. The bigger primary is considered a point mass, and the smaller primary is an unstable elongated primary. The unstable elongated primary refers to the elongated primary rotates about its centre point, i.e. at an instant, the line joining the two ends of the elongated primary and the <i>x</i>-axis makes an angle, <span>\\(\\theta \\in [0,360^\\circ )\\)</span>. Computations of the non-collinear equilibrium points <span>\\(L_{4,5}\\)</span>, and their linear stability, are investigated, and the results are applied to the Jupiter-Amalthea, Saturn-Prometheus and Pluto-Hydra systems. It is found that the positions of the non-collinear equilibrium points <span>\\(L_{4,5}\\)</span> remain unchanged with variation in the angle, <span>\\(\\theta \\)</span>, but small variation in the critical mass parameter, <span>\\(\\mu _c\\)</span> is observed. Variations of the critical mass, <span>\\(\\mu _c\\)</span>, with different segment-length and its rotation are studied. Stable solutions around <span>\\(L_4\\)</span> are obtained in the systems of Jupiter-Amalthea, Saturn-Prometheus, and Pluto-Hydra using the established results.</p>","PeriodicalId":584,"journal":{"name":"Indian Journal of Physics","volume":"4 1","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2024-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Non-collinear equilibrium points in the perturbed restricted three-body problem with unstable elongated primary\",\"authors\":\"Ravi Kumar Verma, Badam Singh Kushvah\",\"doi\":\"10.1007/s12648-024-03383-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we have studied the motion around the non-collinear equilibrium points in the perturbed circular restricted three-body problem. The bigger primary is considered a point mass, and the smaller primary is an unstable elongated primary. The unstable elongated primary refers to the elongated primary rotates about its centre point, i.e. at an instant, the line joining the two ends of the elongated primary and the <i>x</i>-axis makes an angle, <span>\\\\(\\\\theta \\\\in [0,360^\\\\circ )\\\\)</span>. Computations of the non-collinear equilibrium points <span>\\\\(L_{4,5}\\\\)</span>, and their linear stability, are investigated, and the results are applied to the Jupiter-Amalthea, Saturn-Prometheus and Pluto-Hydra systems. It is found that the positions of the non-collinear equilibrium points <span>\\\\(L_{4,5}\\\\)</span> remain unchanged with variation in the angle, <span>\\\\(\\\\theta \\\\)</span>, but small variation in the critical mass parameter, <span>\\\\(\\\\mu _c\\\\)</span> is observed. Variations of the critical mass, <span>\\\\(\\\\mu _c\\\\)</span>, with different segment-length and its rotation are studied. Stable solutions around <span>\\\\(L_4\\\\)</span> are obtained in the systems of Jupiter-Amalthea, Saturn-Prometheus, and Pluto-Hydra using the established results.</p>\",\"PeriodicalId\":584,\"journal\":{\"name\":\"Indian Journal of Physics\",\"volume\":\"4 1\",\"pages\":\"\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2024-08-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indian Journal of Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1007/s12648-024-03383-1\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indian Journal of Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s12648-024-03383-1","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Non-collinear equilibrium points in the perturbed restricted three-body problem with unstable elongated primary
In this paper, we have studied the motion around the non-collinear equilibrium points in the perturbed circular restricted three-body problem. The bigger primary is considered a point mass, and the smaller primary is an unstable elongated primary. The unstable elongated primary refers to the elongated primary rotates about its centre point, i.e. at an instant, the line joining the two ends of the elongated primary and the x-axis makes an angle, \(\theta \in [0,360^\circ )\). Computations of the non-collinear equilibrium points \(L_{4,5}\), and their linear stability, are investigated, and the results are applied to the Jupiter-Amalthea, Saturn-Prometheus and Pluto-Hydra systems. It is found that the positions of the non-collinear equilibrium points \(L_{4,5}\) remain unchanged with variation in the angle, \(\theta \), but small variation in the critical mass parameter, \(\mu _c\) is observed. Variations of the critical mass, \(\mu _c\), with different segment-length and its rotation are studied. Stable solutions around \(L_4\) are obtained in the systems of Jupiter-Amalthea, Saturn-Prometheus, and Pluto-Hydra using the established results.
期刊介绍:
Indian Journal of Physics is a monthly research journal in English published by the Indian Association for the Cultivation of Sciences in collaboration with the Indian Physical Society. The journal publishes refereed papers covering current research in Physics in the following category: Astrophysics, Atmospheric and Space physics; Atomic & Molecular Physics; Biophysics; Condensed Matter & Materials Physics; General & Interdisciplinary Physics; Nonlinear dynamics & Complex Systems; Nuclear Physics; Optics and Spectroscopy; Particle Physics; Plasma Physics; Relativity & Cosmology; Statistical Physics.