Nonlinear Mechanics A Supplement to Theoretical Mechanics of Particles and Continua

ISBN-10: 0486450317

ISBN-13: 9780486450315

Edition: 2006

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Description:

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. This supplement and update of that volume offers a bridge to contemporary mechanics. The original book's focus on continuum mechanics forms the basis for this supplement's discussion of nonlinear continuous systems. 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. 2006 ed.
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Book details

List price: $14.95
Copyright year: 2006
Publisher: Dover Publications, Incorporated
Publication date: 6/16/2006
Binding: Paperback
Pages: 154
Size: 6.50" wide x 9.75" long x 0.50" tall
Weight: 0.484
Language: English

Introduction
Motivation
Nonlinear Continuous Systems
Linearized stability analysis
Rayleigh-Taylor instability
Kelvin-Helmholtz instability
Rayleigh-Benard problem: basic formulation
Boussinesq approximation and thermal expansion
Linearized perturbation equations
Boundary conditions
Rayleigh-Benard problem: linearized theory of convective instability
Proof that solutions are not oscillatory
Vorticity and the eigenvalue equation
Free-free boundary conditions: exact solution
Rigid-rigid boundary conditions: sketch of exact solution
Rayleigh-Benard problem: expansion in Fourier modes
Lorenz equations: direct derivation for simple physical configuration
Discrete Dynamical Systems
Example of a nonlinear oscillator
Duffing oscillator: general form
Duffing oscillator: perturbed simple harmonic oscillator
Phase-space dynamics and fixed points
Action-angle variables
Simple harmonic oscillator
Pendulum
Linearized stability analysis
Lorenz model
Stationary solutions and fixed points
Linearized stability analysis
Periodic oscillatory solutions
Chaotic solutions
Two theorems on phase-space convergence of solutions
Model finite-difference equation: logistic map
Logistic map
Power spectrum
Numerical analysis
Some analytic results
Liouville's theorem revisited
Action-angle variables revisited
Separable, periodic hamiltonian systems
Phase plots and motion on tori
Perturbation of periodic hamiltonian systems
Hamilton-Jacobi theory revisited
Direct perturbation analysis of the anharmonic oscillator
Model one-body problem with time-periodic perturbation
Resonant disruption of phase space
Overlap of disrupted regions
Coupled separable periodic hamiltonian systems
Two weakly coupled degrees of freedom
Resonant disruption of phase space
The Kolmogorov-Arnold-Moser (KAM) theorem
Problems
Problems
References
Index
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