MOTION IN THE GENERALIZED RESTRICTED THREE-BODY PROBLEM
MOTION IN THE GENERALIZED RESTRICTED THREE-BODY PROBLEM
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Date
2011-08
Authors
TAURA, JOEL JOHN
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Abstract
This thesis investigates motion in the generalized restricted three-body problem. It is
generalized in the sense that both the primaries are radiating oblate bodies, together with
the effect of gravitational potential from a belt. It derives the equations of motion, locates
the positions of the equilibrium points and examines their linear stability. It has been found
that in addition to the usual five equilibrium points, there appear two new collinear points
Ln1, n2 L due to the potential from the belt, and in the presence of all these perturbations,
the equilibrium points 1 L , 3 L , 4 L , 5 L come nearer to the primaries; while 2 L , n2 L move
towards the bigger primary and n1 L moves away from it. The collinear equilibrium points
remain unstable, while the triangular points are stable in 0 c and unstable in
1 ,
c 2 where c is the critical mass ratio influenced by the oblateness and radiation of
the primaries and potential from the belt. This model can be applied in the study of binary
systems, especially motion near oblate, radiating binary stars.
Description
A THESIS SUBMITTED TO THE POSTGRADUATE SCHOOL
IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE
AWARD OF MASTERS OF SCIENCE IN MATHEMATICS
DEPARTMENT OF MATHEMATICS
AHMADU BELLO UNIVERSITY
ZARIA
AUGUST 2011
Keywords
MOTION,, GENERALIZED,, RESTRICTED,, THREE-BODY,, PROBLEM.