In their prior Dover book, the authors provided a self-contained account of classical mechanics; this supplement/update offers a bridge to contemporary mechanics. Topics include nonlinear continuous systems. 2006 edition.
In their prior Dover book, the authors provided a self-contained account of classical mechanics; this supplement/update offers a bridge to contemporary mechanics. Topics include nonlinear continuous systems. 2006 edition.
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
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
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