Nonlinear Mechanics: A Supplement to Theoretical Mechanics of Particles and Continua

by Alexander L. Fetter, John Dirk Walecka

Overview

In their prior Dover book, Theoretical Mechanics of Particles and Continua, Alexander L. Fetter and John Dirk Walecka provided a lucid and self-contained account of classical mechanics, together with appropriate mathematical methods. This supplement—an update of that volume—offers a bridge to contemporary mechanics.
The original book's focus on continuum mechanics—with chapters on sound waves in fluids, surface waves on fluids, heat conduction, and viscous fluids—forms the basis for this supplement's discussion of nonlinear continuous systems. Topics include linearized stability analysis; a detailed examination of the Rayleigh-Bénard problem, from its formulation to issues of linearized theory of convective instability and expansion in Fourier modes; and the direct derivation of Lorenz equations for simple physical configuration. The first half of the original text deals with particle mechanics, and this supplement returns to the study of systems with a finite number of degrees of freedom. A concluding section presents a series of problems that reinforce the supplement's teachings.

Product Details

ISBN-13:	9780486136998
Publisher:	Dover Publications
Publication date:	04/06/2012
Series:	Dover Books on Physics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	160
File size:	8 MB

Table of Contents

Part 1. Introduction
1. Motivation
Part 2. Nonlinear Continuous Systems
2. Linearized stability analysis
3. Rayleigh-Bénard problem: basic formulation
4. Rayleigh-Bénard problem: linearized theory of convective instability
5. Rayleigh-Bénard problem: expansion in Fourier modes
6. Lorenz equations: direct derivation for simple physical configuration
Part 3. Discrete Dynamical Systems
7. Example of a nonlinear oscillator
8. Phase-space dynamics and fixed points
9. Lorenz model
10. M odel finite-difference equation: logistic map
11. Liouville's theorem revisited
12. Action-angle variables revisited
13. Perturbation of periodic Hamiltonian systems
14. Coupled separable periodic Hamiltonian systems
Part 4. Problems
References
Index