Chaotic Dynamics In Hamiltonian Systems: With Applications To Celestial Mechanics

With Applications to Celestial Mechanics

Harry Dankowicz

• Publisher: World Scientific
• Year: 1997
• ISBN:
  9789812796288
• Topic: Physical Sciences
• Subtopic: Chaotic Behavior in Systems

In the past hundred years investigators have learned the significance of complex behavior in deterministic systems. The potential applications of this discovery are as numerous as they are encouraging.This text clearly presents the mathematical foundations of chaotic dynamics, including methods and results at the forefront of current research. The book begins with a thorough introduction to dynamical systems and their applications. It goes on to develop the theory of regular and stochastic behavior in higher-degree-of-freedom Hamiltonian systems, covering topics such as homoclinic chaos, KAM theory, the Melnikov method, and Arnold diffusion. Theoretical discussions are illustrated by a study of the dynamics of small circumasteroidal grains perturbed by solar radiation pressure. With alternative derivations and proofs of established results substituted for those in the standard literature, this work serves as an important source for researchers, students and teachers.Skillfully combining in-depth mathematics and actual physical applications, this book will be of interest to the applied mathematician, the theoretical mechanical engineer and the dynamical astronomer alike.

Table of contents

• Contents
• Preface
• Chapter 1 INTRODUCTION
• Chapter 2 HAMILTONIAN SYSTEMS
• Chapter 3 HOMOCLINIC ORBITS
• Chapter 4 THE PERTURBATION APPROACH - 1 1/2 DEGREES-OF-FREEDOM
• Chapter 5 APPLICATION - RADIATION PRESSURE PROBLEMS IN CELESTIAL MECHANICS. PART I
• Chapter 6 GEOMETRY AND DYNAMICS IN MANY DEGREES OF FREEDOM
• Chapter 7 APPLICATION - RADIATION PRESSURE PROBLEMS IN CELESTIAL MECHANICS. PART II
• Outlook
• Index