EXISTENCE AND LINEAR STABILITY OF EQUILIBRIUM POINTS IN THE PHOTOGRAVITATIONAL RESTRICTED THREE-BODY PROBLEM WITH POYNTING-ROBERTSON DRAG AND OBLATENESS

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Date
2014-08
Authors
TAJUDEEN, OLUWAFEMI AMUDA
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Abstract
This research work investigates the existence and linear stability of a test particle of infinitesimal mass around the equilibrium points in the photogravitational restricted three body problem with Poynting-Robertson (P-R) drag and oblateness. The primaries are modelled as an oblate spheroid and a radiating mass. The equations of motion are model such that the equilibrium points and linear stability can be study. It is seen that three points lying on the line joining the primaries (collinear equilibrium points) exist and depend only on the radiation pressure force of the smaller primary, oblateness of the bigger primary and the mass parameter of the system. Aside the collinear points, a pair of equilibrium points (triangular equilibrium points) forming triangles with the line joining the primaries, exist and are defined by the mass parameter, oblateness of the bigger primary, radiation pressure and P-R drag of the smaller primary. Further, the equilibrium points lying out of the orbital plane of motion (out-of-plane equilibrium points) was found. The linear stability of the equilibrium points is studied. The collinear equilibrium points are unstable due to a positive root of the governing characteristic equation. The triangular and the out-of-plane equilibrium points are also unstable due to positive real part of the complex roots and a positive root. In general, all these forces; that is, the oblateness of the bigger primary, radiation and P-R drag, are destabilizing forces. Further, the numerical explorations are performed in order to give precise and accurate results about the positions of the equilibrium points and their stability for different systems.
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A THESIS SUBMITTED TO THE SCHOOL OF POSTGRADUATE STUDIES, AHMADU BELLO UNIVERSITY, ZARIA IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF A MASTER OF SCIENCE DEGREE IN MATHEMATICS, DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCES, AHMADU BELLO UNIVERSITY, ZARIA NIGERIA
Keywords
LINEAR STABILITY,, EQUILIBRIUM POINTS,, PHOTOGRAVITATIONAL,, THREE-BODY PROBLEM,, POYNTING-ROBERTSON DRAG,, OBLATENESS,
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