From Ordered to Chaotic Motion in Celestial Mechanics

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.

Contents:

• Qualitative Analyses on Motion in 3-Body System:

  • Equations of Motion and Invariants
  • Condition of Permissible Motion
  • Variations of Configuration and Position
  • Restricted 3-Body Problem and Singular Points of Motion
  • Stabilities of Lagrange and Euler Solutions
  • Elliptic Restricted 3-Body Problem
  • Hill Region in 3-Body Problem
  • Evolution of Inertia Momentum in N-Body Problem
  • Motion of Isolated Body in 3-Body Problem
  • Sitnikov Motion and Its Generalization
  • Central Configuration of 4-Body Problem
  • Central Configuration of N-Body Problem with General Attraction and Homographic Solutions

• Motion of Small Bodies in the Planetary System:

  • Mapping Method in Hamiltonian System
  • Structure of Phase Space Near Lagrange Solutions
  • Stability of Asteroid Orbits in Resonances
  • Shepherding of Uranian Ring
  • Formation of Kuiper Belt
  • Dynamics of Neptune Trojans
  • Apsidal and Nodal Resonances in Multiple
  • Aspidal Corotation in 3:1 Mean Motion Resonance

• Chaotic Motion of Orbits:

  • Conservative Dynamical System
  • Ordered and Chaotic Motion
  • Poincaré Surface of Section
  • Ordered and Chaotic Motion of Stars
  • Application of Mapping Method to Comet Motion
  • Global Applicability of Symplectic Integrator
  • Transfer of Comet Orbit
  • Random Walk in Comet Motion
  • Chaotic Region of Encounter-Type Orbit

• Orbit Diffusion:

  • Diffusion in Comet Motion
  • KS Entropy of Area-Preserving Mapping
  • Invariant Tori in Volume-Preserving Mapping
  • Perturbed Extension of Area-Preserving Mapping
  • KS Entropy of Volume-Preserving Mapping
  • Attractor in Three-Dimension Mapping
  • Stickiness Effect and Hyperbolic Structure (I)
  • Stickiness Effect and Hyperbolic Structure (II)
  • Diffusion in Four-Dimensional Mapping

Readership: Graduate students and researchers interested in astrophysics, astronomy, or celestial mechanics.
Key Features:

• The author Professor Sun is a senior scientist in celestial mechanics and nonlinear dynamics
• The book presents interdisciplinary research works with all the materials from the research works of the authors
• The book contains both pure theoretical analyses and numerical analyses