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Stability and bifurcations of symmetrical 3D-periodic orbits in the Sitnikov five-body problem.

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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]
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Database: Engineering Source
Description
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]
ISSN:0004640X
DOI:10.1007/s10509-026-04557-5