World Scientific Series on Nonlinear Science, Series A - Vol. 25
CHAOTIC DYNAMICS IN HAMILTONIAN SYSTEMS
With Applications to Celestial Mechanics
by Harry Dankowicz (Royal Institute of Technology, Sweden)
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.
Contents:
- Introduction
- Hamiltonian Systems
- Homoclinic Orbits
- The
Perturbation Approach
- Application — Radiation Pressure I
- Geometry and Dynamics in Many Degrees-of-Freedom
- Application — Radiation Pressure II
- Outlook
- Index
Readership: Students and researchers in dynamical systems, classical mechanics
and dynamical astronomy.
| 224pp |
Pub. date: Dec 1997 |
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