{"title":"N层异质三轴刚体的扰动势能对R3BP中枰点稳定性的影响","authors":"Kumari Shalini , Pankaj Sharma , Kumari Ranjana","doi":"10.1016/j.newast.2024.102202","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we investigate the motion of an infinitesimal mass <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> in the restricted three-body problem by taking both the primaries as heterogeneous triaxial rigid bodies with <em>N</em> layers. The potential of the proposed model and the equations of motion for the infinitesimal mass <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> are derived. Our findings reveal the existence of five libration points denoted as <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> <span><math><mrow><mo>(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow></math></span> in the proposed model, with three being collinear and two being non-collinear. We observed that the collinear libration points <span><math><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mrow><mo>(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow></mrow></math></span> are unstable, whereas the non-collinear libration points <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>4</mn><mo>,</mo><mn>5</mn></mrow></msub></math></span> are conditionally stable for the mass parameter <span><math><mrow><mi>μ</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span>, where <span><math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>25681</mn><mspace></mspace><msub><mrow><mi>k</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>−</mo><mn>1</mn><mo>.</mo><mn>31619</mn><mspace></mspace><msub><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>−</mo><mn>2</mn><mo>.</mo><mn>24318</mn><mspace></mspace><msub><mrow><mi>k</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>−</mo><mn>6</mn><mo>.</mo><mn>10258</mn><mspace></mspace><msub><mrow><mi>k</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math></span>.</p></div>","PeriodicalId":54727,"journal":{"name":"New Astronomy","volume":"109 ","pages":"Article 102202"},"PeriodicalIF":1.9000,"publicationDate":"2024-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Effect of perturbed potential of heterogeneous triaxial rigid bodies of N layers on the stability of libration points in the R3BP\",\"authors\":\"Kumari Shalini , Pankaj Sharma , Kumari Ranjana\",\"doi\":\"10.1016/j.newast.2024.102202\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we investigate the motion of an infinitesimal mass <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> in the restricted three-body problem by taking both the primaries as heterogeneous triaxial rigid bodies with <em>N</em> layers. The potential of the proposed model and the equations of motion for the infinitesimal mass <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> are derived. Our findings reveal the existence of five libration points denoted as <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> <span><math><mrow><mo>(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow></math></span> in the proposed model, with three being collinear and two being non-collinear. We observed that the collinear libration points <span><math><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mrow><mo>(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow></mrow></math></span> are unstable, whereas the non-collinear libration points <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>4</mn><mo>,</mo><mn>5</mn></mrow></msub></math></span> are conditionally stable for the mass parameter <span><math><mrow><mi>μ</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span>, where <span><math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>25681</mn><mspace></mspace><msub><mrow><mi>k</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>−</mo><mn>1</mn><mo>.</mo><mn>31619</mn><mspace></mspace><msub><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>−</mo><mn>2</mn><mo>.</mo><mn>24318</mn><mspace></mspace><msub><mrow><mi>k</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>−</mo><mn>6</mn><mo>.</mo><mn>10258</mn><mspace></mspace><msub><mrow><mi>k</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math></span>.</p></div>\",\"PeriodicalId\":54727,\"journal\":{\"name\":\"New Astronomy\",\"volume\":\"109 \",\"pages\":\"Article 102202\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2024-02-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"New Astronomy\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1384107624000162\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ASTRONOMY & ASTROPHYSICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"New Astronomy","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1384107624000162","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 0
摘要
在本文中，我们研究了受限三体问题中无穷小质量 m3 的运动，将两个基体均视为具有 N 层的异质三轴刚体。本文推导了所提模型的势和无穷小质量 m3 的运动方程。我们的研究结果表明，在所提出的模型中存在五个天平动点，用 Li（i=1,2,3,4,5）表示，其中三个为共线天平动点，两个为非共线天平动点。我们观察到，对于质量参数μ∈（0,μc），其中μc=0.25681k1-1.31619k2-2.24318k3-6.10258k4，共线枰点Li(i=1,2,3)是不稳定的，而非共线枰点L4,5是有条件稳定的。
Effect of perturbed potential of heterogeneous triaxial rigid bodies of N layers on the stability of libration points in the R3BP
In this paper, we investigate the motion of an infinitesimal mass in the restricted three-body problem by taking both the primaries as heterogeneous triaxial rigid bodies with N layers. The potential of the proposed model and the equations of motion for the infinitesimal mass are derived. Our findings reveal the existence of five libration points denoted as in the proposed model, with three being collinear and two being non-collinear. We observed that the collinear libration points are unstable, whereas the non-collinear libration points are conditionally stable for the mass parameter , where .
期刊介绍：
New Astronomy publishes articles in all fields of astronomy and astrophysics, with a particular focus on computational astronomy: mathematical and astronomy techniques and methodology, simulations, modelling and numerical results and computational techniques in instrumentation.
New Astronomy includes full length research articles and review articles. The journal covers solar, stellar, galactic and extragalactic astronomy and astrophysics. It reports on original research in all wavelength bands, ranging from radio to gamma-ray.
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