# American Institute of Mathematical Sciences

December  2015, 8(6): 1047-1054. doi: 10.3934/dcdss.2015.8.1047

## Stability of equilibria points for a dumbbell satellite when the central body is oblate spheroid

 1 National Research Institute of Astronomy and Geophysics, Cairo 2 Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Hospital de Marina, 30203-Cartagena, Región de Murcia 3 Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah

Received  May 2015 Revised  August 2015 Published  December 2015

The main aim of the present work is to study the positions of the equilibria points and their stability in the frame work of satellite approximation. The significant implication is that the motion around these points is unstable in the linear sense. The principle of angular momentum conservation is used as a tool to reduce the degree of freedom of the dynamical systems of equations. The positions of the relative equilibria are explicitly found as well as necessary and sufficient conditions for stable motion in the linear sense are stated.
Citation: Elbaz I. Abouelmagd, Juan L. G. Guirao, Aatef Hobiny, Faris Alzahrani. Stability of equilibria points for a dumbbell satellite when the central body is oblate spheroid. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1047-1054. doi: 10.3934/dcdss.2015.8.1047
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