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Classical Mechanics: A Computational Approach >> Content Detail



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Calendar

This section lists the lecture topics for the course, organized by general topic areas.
Introduction

LEC #TOPICS
1Mechanics is More than Equations of Motion


Lagrangian Mechanics

LEC #TOPICS
2Principle of Stationary Action
3Lagrange Equations
4Hamilton's Principle
5Coordinate Transformations and Rigid Constraints
6Total-time Derivatives and the Euler-Lagrange Operator
7State and Evolution - Chaos
8Conserved Quantities


Rigid Bodies

LEC #TOPICS
9Kinematics of Rigid Bodies, Moments of Inertia
10Generalized Coordinates for Rigid Bodies
11Motion of a Free Rigid Body
12Axisymmetric Top
13Spin-Orbit Coupling
14Euler's Equations


Hamiltonian Mechanics

LEC #TOPICS
15Hamilton's Equations
16Legendre Transformation
17Hamiltonian Action and Poisson Brackets
18Phase Space Reduction
19Phase-Space Evolution, Surfaces of Section
20Autonomous Systems: Henon-Heiles
21Exponential Divergence, Solar System
22Liouville Theorem


Phase Space Structure

LEC #TOPICS
23Linear Stability
24Homoclinic Tangle
25Integrable Systems
26Poincare-Birkhoff Theorem
27Invariant Curves -- KAM Theorem


Canonical Transformations

LEC #TOPICS
28Canonical Transformations
29Integral Invariants, Extended Phase Space
30Generating Functions
31Time Evolution is Canonical
32Hamilton-Jacobi Equation
33Lie Transforms


Perturbation Theory

LEC #TOPICS
34Perturbation Theory with Lie Series
35Small Denominators and Secular Terms
36Nonlinear Resonances and Resonance Overlap
37Second-Order Resonances
38Adiabatic Chaos



 



 








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