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