The Restricted Five-Body Problem With Cyclic Kite Configuration. Issue 1 (2nd January 2019)

• Record Type: Journal Article
• Authors: Ansari, Abdullah A.; Alhussain, Ziyad A.
• Is Part Of: Journal of dynamical systems and geometric theories. Volume 17:Issue 1(2019)
• Page Start: 91
• Page End: 107
• Publication Date: 2019-01-02
• Subjects: 70F05 -- 70F15; Five-body Problem -- Cyclic kite configuration -- Equilibrium points -- Zero-velocity curves -- Regions of motion -- Poincare surfaces of section -- Basins of attraction -- Stability; Differentiable dynamical systems -- Periodicals; Geometry -- Periodicals; Differentiable dynamical systems; Geometry; Periodicals; 515.39
• DOI: 10.1080/1726037X.2018.1551720
• Languages: English
• ISSNs: 1726-037X

Abstract

ABSTRACT: This manuscript investigates the five-body problem with kite configuration where four bodies are placed at the vertices of a kite. All the vertices of kite are taken at the circumference of a circle. These four bodies are considered as primaries which are moving on the circle with same centre which is taken as origin. The fifth infinitesimal body is moving in the space under the influences of these four primaries but not influencing them. After evaluating the equations of motion of the infinitesimal body, we have determined the Jacobi-integral. In the next section, we have done the computational works, where we have plotted the locations of equilibrium points, zero-velocity curves, regions of motion, Poincaré surfaces of section and basins of attraction in different planes (in-plane and out-of-planes). Moreover, we have examined the linear stability of all the equilibrium points and found that all the equilibrium points are unstable.