Stability and bifurcations of symmetrical 3D-periodic orbits in the Sitnikov five-body problem.
Saved in:
| Title: | Stability and bifurcations of symmetrical 3D-periodic orbits in the Sitnikov five-body problem. |
|---|---|
| Authors: | Pandey, L. P.1 (AUTHOR) lppandey16april@gmail.com, Sharma, Binay Kumar2 (AUTHOR) binay.sharma@sbs.du.ac.in, Tomar, Rahul3 (AUTHOR) rahultomar@ramjas.du.ac.in |
| Source: | Astrophysics & Space Science. Mar2026, Vol. 371 Issue 3, p1-16. 16p. |
| Subjects: | Bifurcation theory, Many-body problem, Lagrangian points, Combinatorial dynamics, Orbits (Astronomy), Floquet theory, Dynamic stability |
| Abstract: | We have studied the variations in stability, bifurcation, critical velocity, Lagrange points, and critical periodic orbits in the context of the transition from the Sitnikov four-body system (as analyzed by Soulis et al. (Celest. Mech. Dyn. Astron. 100:251–266, 2008)) to the Sitnikov five-body system. The incorporation of one primary body results in a reduction in critical velocity and an increase in the number of stability intervals. We applied Floquet's theory to study the stability/instability of the motion of negligible mass. For this, we assume z i n as family parameter and vary it in the interval [ 0 , 10 ]. Upon slightly perturbing the negligible mass from the z-axis, we obtained 13 Lagrange points. We have determined three-dimensional families of periodic orbits which bifurcate from the critical points/bifurcation points. We observed that the bifurcation points lie within the interval [ 1.0709360 , 2.7944120 ]. We have discussed stability/instability of periodic orbits bifurcating from the critical points. [ABSTRACT FROM AUTHOR] |
| Copyright of Astrophysics & Space Science is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 192984028 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Stability and bifurcations of symmetrical 3D-periodic orbits in the Sitnikov five-body problem. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Pandey%2C+L%2E+P%2E%22">Pandey, L. P.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> lppandey16april@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Sharma%2C+Binay+Kumar%22">Sharma, Binay Kumar</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> binay.sharma@sbs.du.ac.in</i><br /><searchLink fieldCode="AR" term="%22Tomar%2C+Rahul%22">Tomar, Rahul</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> rahultomar@ramjas.du.ac.in</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Astrophysics+%26+Space+Science%22">Astrophysics & Space Science</searchLink>. Mar2026, Vol. 371 Issue 3, p1-16. 16p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Bifurcation+theory%22">Bifurcation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Many-body+problem%22">Many-body problem</searchLink><br /><searchLink fieldCode="DE" term="%22Lagrangian+points%22">Lagrangian points</searchLink><br /><searchLink fieldCode="DE" term="%22Combinatorial+dynamics%22">Combinatorial dynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Orbits+%28Astronomy%29%22">Orbits (Astronomy)</searchLink><br /><searchLink fieldCode="DE" term="%22Floquet+theory%22">Floquet theory</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamic+stability%22">Dynamic stability</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We have studied the variations in stability, bifurcation, critical velocity, Lagrange points, and critical periodic orbits in the context of the transition from the Sitnikov four-body system (as analyzed by Soulis et al. (Celest. Mech. Dyn. Astron. 100:251–266, 2008)) to the Sitnikov five-body system. The incorporation of one primary body results in a reduction in critical velocity and an increase in the number of stability intervals. We applied Floquet's theory to study the stability/instability of the motion of negligible mass. For this, we assume z i n as family parameter and vary it in the interval [ 0 , 10 ]. Upon slightly perturbing the negligible mass from the z-axis, we obtained 13 Lagrange points. We have determined three-dimensional families of periodic orbits which bifurcate from the critical points/bifurcation points. We observed that the bifurcation points lie within the interval [ 1.0709360 , 2.7944120 ]. We have discussed stability/instability of periodic orbits bifurcating from the critical points. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Astrophysics & Space Science is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=192984028 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10509-026-04557-5 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 1 Subjects: – SubjectFull: Bifurcation theory Type: general – SubjectFull: Many-body problem Type: general – SubjectFull: Lagrangian points Type: general – SubjectFull: Combinatorial dynamics Type: general – SubjectFull: Orbits (Astronomy) Type: general – SubjectFull: Floquet theory Type: general – SubjectFull: Dynamic stability Type: general Titles: – TitleFull: Stability and bifurcations of symmetrical 3D-periodic orbits in the Sitnikov five-body problem. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Pandey, L. P. – PersonEntity: Name: NameFull: Sharma, Binay Kumar – PersonEntity: Name: NameFull: Tomar, Rahul IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 0004640X Numbering: – Type: volume Value: 371 – Type: issue Value: 3 Titles: – TitleFull: Astrophysics & Space Science Type: main |
| ResultId | 1 |
