This book provides a brief introduction to some basic but important problems in celestial mechanics, and particularly in the few-body problem, such as the permissible and forbidden region of motion, the evolution of moment of inertia of a system, and the orbital stability of asteroids in the solar system. All these are based on some main results in the authors' research works, which are related to the qualitative method of celestial mechanics and nonlinear dynamics. Some of these works are interdisciplinary, involving celestial mechanics, nonlinear dynamics and other disciplines. The book covers a variety of topics for dynamics in the solar system, including the comets, asteroids, planetary rings, Trojan asteroids, etc.
As a senior scientist, Professor Sun shares his research experiences in this book. Readers may find plenty of information both about the theoretical and numerical analyses in celestial mechanics, and about the applications of theories and methods to dynamical problems in astronomy.
Qualitative Analyses on Motion in Three-body System: Equation of Motion and Invariant; Condition of Permissible Motion; Variations of Configuration and Position; Hill Region in Three-body Problem; Evolution of Inertia Momentum in N-body Problem; Motion of Isolated Body in Three-body Problem; Hill Stability in Hierarchical Triple System; Sitnikov Motion and its Generalization; Central Configuration of 4-body Problem; Central Configuration of N-body Problem with General Attraction and the Homographic Solutions; Motion of Small Bodies in the Planetary System: Restricted 3-body Problem; Lagrange and Euler Solutions and Their Stabilities; Elliptic Restricted Three-body Problem; Structure of Phase Space Near Lagrange Solutions; Mapping Method in Hamiltonian System; Shepherding of Uranian Ring; Stability of Asteroid Orbits in Resonances; Formation of Kuiper Belt; Effect of Resonance in Kuiper Belt; Stochastic Effects in Kuiper Belt; Dynamics of Neptune Trojans; Apsidal and Nodal Resonance; Aspidal Corotation in Resonance; Chaotic Motion and Orbit Diffusion: Conservative System; Ordered and Chaotic Motion; Poincare Section; Chaotic Motion of Stars; Chaotic Behavior in Comet Motion; Diffusion in Comet Motion; Transfer of Comet Orbit; Chaotic Region of Encounter-type Orbit; KS Entropy of Area-preserving Mapping; Invariant Tori in Volume-preserving Mapping; Perturbed Extension of Area-preserving Mapping (I, II, III); KS Entropy of Volume-preserving Mapping; Attractor in Three-dimensional Mapping; Diffusion in Four-dimensional Mapping; Diffusion in Symplectic Mapping; Global Applicability of Symplectic Integrator; Stickiness Effect and Hyperbolic Structure; Stickiness Effect in Three-dimensional Mapping;
