Periodic orbits around the collinear libration points

Volume 9, Issue 4, pp 1716--1727 http://dx.doi.org/10.22436/jnsa.009.04.27

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Authors

E. I. Abouelmagd - Celestial Mechanics Unit, Astronomy Department, National Research Institute of Astronomy and Geophysics (NRIAG), Helwan, Cairo, Egypt. - Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia. F. Alzahrani - Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia. A. Hobiny - Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia. J. L. G. Guirao - Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Hospital de Marina, 30203 Cartagena, Región de Murcia, Spain. M. Alhothuali - Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia.

Abstract

The locations for the collinear libration points in the framework of the restricted three-body problem are determined when the bigger primary is a triaxial rigid body. The analysis of the periodic motion around these points is performed and given up to second order in the case that the initial state of the motion gives rise to periodic orbits. Moreover, some numerical results for the locations of collinear points are provided and the graphical investigations for the periodic motion are plotted, as well. It is worth mentioning that the collinear libration points and associated periodic orbits are considered the optimal placement to transfer a spacecraft to the nominal periodic orbits or to an associated stable manifold.

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Keywords

• Restricted three-body problem
• collinear points
• periodic orbits.

MSC

•  70E17
•  70E20
•  70E40
•  37C27

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