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Nonlinear Mechanics
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35 b
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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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