Summary
Chapter 1 GENERAL INTRODUCTION Introduction
1.1 Notations and Symbols
1.2 Definitions
1.3 Theorems of The Stability of
Linear and Non-Linear Systems
Chapter 2 EFFECT OF PERTURBATIONS ON THE
LOCATIONS AND LINEAR STABILITY
OF EQUILIBRIUM POINTS OF THE
RESTRICTED THREE BODY PROBLEM Introduction
2.1 Effect of Perturbation in the Coriolis
Force on the Locations and Stability of
Equilibrium Points
2.1.1 Equations of Motion
2.1.2 Locations of Equilibrium points
2.1.3 Stability of Equilibrium Points
2.1.4 Conclusions
2.2 Effect of Perturbations in Coriolis and
Centrifugal forces on the Existence
and Stability of Equilibrium Points in
the Restricted Problem
Introduction
2.2.1 Equations of motion
2.2.2 Equilibrium points
2.2.3 Critical Mass Ratio
2.2.4 Conclusions
2.3 Stability of the Triangular Points when
the Bigger Primary is an Oblate Spheroid
Introduction
2.3.1 Equations of Motion
2.3.2 Equilibrium Points
2.3.3 Critical Mass Ratio and Stability
of Triangular Points
2.3.4 Conclusions
2.4 Photo-gravitational Restricted
Three-Body Problem
Introduction
2.4.1 Equations of Motion
2.4.2 Location of Equilibrium Points
2.4.3 Stability of Equilibrium Points
2.5 Effect of Perturbed Potentials on the
Stability of Equilibrium Points in the
Restricted Problem
Introduction
2.5.1 Perturbed Potential and the Mean Motion of the Primaries
2.5.2 Equations of Motion
2.5.3 Location of Equilibrium Points
2.5.4 Stability of Equilibrium Points
2.5.5 Applications
Chapter 3 EFFECT OF PERTURBATIONS ON THE
NON-LINEAR STABILITY OF EQUILIBRIUM POINTS OF
RESTRICTED PROBLEM
Introduction
3.1 Effect of Perturbations in Coriolis and
Centrifugal Forces on the Non-Linear
Stability of Equilibrium Points in the
Restricted Three Problem
Introduction
3.1.1 First Order Normalization
3.1.2 Second Order Normalization
3.1.3 Second Order Coefficients in the Frequencies
3.1.4 Stability
3.1.5 Conclusion
3.2 Effect of Oblateness on the Non-Linear
Stability of Triangular Equilibrium Point
L4 in the Restricted Problem Introduction
3.2.1 Equations of Motion and Non-Linear Stability
3.2.2 Conclusions
3.3 Non-Linear Stability in the Generalized
Restricted Three-Body Problem
3.3.1 Conclusions
Chapter 4 EFFECT OF TRIAXIALITY OF THE
PRIMARIES ON THE EXISTENCE AND
STABILITY OF EQUILIBRIUM POINTS
IN THE RESTRICTED THREE-BODY
PROBLEM
Introduction
4.1 Existence and Stability of Equilibrium
points in the Restricted Three-Body
Problem when the Smaller Primary
is a Triaxial Rigid Body
Introduction
4.1.1 Equations of Motion
4.1.2 Location of Equilibrium Points
4.1.3 Stability of Equilibrium Points
4.1.4 Conclusions
4.2 Existence and Stability of Equilibrium
Points in the Restricted three-Body
Problem When the Smaller Primary
is a Triaxial Rigid Body and the Bigger
one an Oblate Spheroid
Introduction
4.2.1 Equations of Motion
4.2.2 Location of Equilibrium Points
4.2.3 Conclusion
4.3 Existence and Stability of Equilibrium
Points in the Restricted Three Body
Problem When the Primaries are
Triaxial Bodies
Introduction
4.3.1 Location of Equilibrium Points and the Critical Pass Ratio
4.3.2 Conclusions
4.4 The Non-Linear Stability of L4 in the
Restricted Three-Body Problem when
the Bigger Primary is a Triaxial Rigid Body
Introduction
4.4.1 Location of Triangular Point L4 and Lagrangian of the System
4.4.2 Conclusions
4.5 Non-Linear Stability of/-,4 in the
Restricted Three Body Problem when
the Bigger Primary is a Triaxial Rigid
Body and a source of radiation or both
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