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 the primaries are triaxial rigid bodies 4.5.1 The Non-Linear Stability of L4 in the Restricted Three Body Problem When the bigger Primary is a Triaxial Rigid Body and source of radiation 4.5.2 The Non-Linear Stability of L4 in the Restricted Three Body Problem When both the Primaries are Triaxial Rigid Bodies REFERENCES 編輯手記
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