Geography of order and chaos in mechanics investigations of quasi-integrable systems with analytical, numerical, and graphical tools Bruno Cordani

Format:

Book

Author/Creator:

Cordani, Bruno, 1945-

Series:

Progress in mathematical physics v. 64

Language:

English

Subjects (All):

Mathematical physics.

Differential equations.

Physical Description:

1 online resource

Place of Publication:

New York, NY Birkhäuser ©2013

Summary:

This original monograph aims to explore the dynamics in the particular but very important and significant case of quasi-integrable Hamiltonian systems, or integrable systems slightly perturbed by other forces. With both analytic and numerical methods, the book studies several of these systems--including for example the hydrogen atom or the solar system, with the associated Arnold web--through modern tools such as the frequency-modified fourier transform, wavelets, and the frequency-modulation indicator. Meanwhile, it draws heavily on the more standard KAM and Nekhoroshev theorems. Geography of Order and Chaos in Mechanics contains many figures that illuminate its concepts in novel ways, but perhaps its most useful feature is its inclusion of software to reproduce the various numerical experiments. The graphical user interfaces of five supplied MATLAB programs allows readers without any knowledge of computer programming to visualize and experiment with the distribution of order, chaos and resonances in various Hamiltonian systems. This monograph will be a valuable resource for professional researchers and certain advanced undergraduate students in mathematics and physics, but mostly will be an exceptional reference for Ph. D. students with an interest in perturbation theory

Contents:

Introductory Survey Analytical Mechanics and Integrable Systems Perturbation Theory Numerical Tools I: ODE Integration Numerical Tools II: Detecting Order, Chaos, and Resonances The Kepler Problem The KEPLER Program Some Perturbed Keplerian Systems The Multi-Body Gravitational Problem Final Remarks and Perspectives

Notes:

Includes bibliographical references and index

Other Format:

Print version:

ISBN:

9780817683702

0817683704

0817683690

9780817683696

9781283909921

1283909928

OCLC:

812453211

Access Restriction:

Restricted for use by site license