This section lists the lecture topics for the course, organized by general topic areas.
Introduction
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| LEC # | | | | TOPICS |
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| | | | 1 | | | | Mechanics is More than Equations of Motion | | | |
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Lagrangian Mechanics
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| LEC # | | | | TOPICS |
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| | | | 2 | | | | Principle of Stationary Action | | | | | | | | 3 | | | | Lagrange Equations | | | | | | | | 4 | | | | Hamilton's Principle | | | | | | | | 5 | | | | Coordinate Transformations and Rigid Constraints | | | | | | | | 6 | | | | Total-time Derivatives and the Euler-Lagrange Operator | | | | | | | | 7 | | | | State and Evolution - Chaos | | | | | | | | 8 | | | | Conserved Quantities | | | |
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Rigid Bodies
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| LEC # | | | | TOPICS |
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| | | | 9 | | | | Kinematics of Rigid Bodies, Moments of Inertia | | | | | | | | 10 | | | | Generalized Coordinates for Rigid Bodies | | | | | | | | 11 | | | | Motion of a Free Rigid Body | | | | | | | | 12 | | | | Axisymmetric Top | | | | | | | | 13 | | | | Spin-Orbit Coupling | | | | | | | | 14 | | | | Euler's Equations | | | |
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Hamiltonian Mechanics
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| LEC # | | | | TOPICS |
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| | | | 15 | | | | Hamilton's Equations | | | | | | | | 16 | | | | Legendre Transformation | | | | | | | | 17 | | | | Hamiltonian Action and Poisson Brackets | | | | | | | | 18 | | | | Phase Space Reduction | | | | | | | | 19 | | | | Phase-Space Evolution, Surfaces of Section | | | | | | | | 20 | | | | Autonomous Systems: Henon-Heiles | | | | | | | | 21 | | | | Exponential Divergence, Solar System | | | | | | | | 22 | | | | Liouville Theorem | | | |
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Phase Space Structure
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| LEC # | | | | TOPICS |
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| | | | 23 | | | | Linear Stability | | | | | | | | 24 | | | | Homoclinic Tangle | | | | | | | | 25 | | | | Integrable Systems | | | | | | | | 26 | | | | Poincare-Birkhoff Theorem | | | | | | | | 27 | | | | Invariant Curves -- KAM Theorem | | | |
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Canonical Transformations
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| LEC # | | | | TOPICS |
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| | | | 28 | | | | Canonical Transformations | | | | | | | | 29 | | | | Integral Invariants, Extended Phase Space | | | | | | | | 30 | | | | Generating Functions | | | | | | | | 31 | | | | Time Evolution is Canonical | | | | | | | | 32 | | | | Hamilton-Jacobi Equation | | | | | | | | 33 | | | | Lie Transforms | | | |
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Perturbation Theory
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| LEC # | | | | TOPICS |
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| | | | 34 | | | | Perturbation Theory with Lie Series | | | | | | | | 35 | | | | Small Denominators and Secular Terms | | | | | | | | 36 | | | | Nonlinear Resonances and Resonance Overlap | | | | | | | | 37 | | | | Second-Order Resonances | | | | | | | | 38 | | | | Adiabatic Chaos | | | |
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