Readings

All readings are taken from the course textbook:

Buy at Amazon Sussman, Gerald Jay, and Jack Wisdom. Structure and Interpretation of Classical Mechanics. Cambridge, MA: MIT Press, 2001. ISBN: 9780262194556.

The full text is available here (MIT Press website).

Errata for SICM

Use the Table of Contents to find each section listed in the table below.

SES # TOPICS READINGS
1 Mechanics is more than equations of motion Notation appendix, Scheme appendix, sections 1 through 1.4
Lagrangian mechanics
2 Principle of stationary action  
3 Lagrange equations Section 1.5
4 Hamilton's principle Sections 1.6 up to 1.6.2
5 Coordinate transformations and rigid constraints Sections 1.6.2, 1.6.3
6 Total-time derivatives and the Euler-Lagrange operator Section 1.6.4
7 State and evolution: chaos Section 1.7
8 Conserved quantities Section 1.8
Rigid bodies
9 Kinematics of rigid bodies, moments of inertia Sections 2.1, 2.2, 2.3, 2.4, 2.5
10 Generalized coordinates for rigid bodies Sections 2.6, 2.7
11 Motion of a free rigid body Sections 2.8, 2.9
12 Axisymmetric top Section 2.10
13 Spin-orbit coupling Sections 2.11, 2.12
Hamiltonian mechanics
14 Hamilton's equations Sections 3.1 up to 3.1.1
15 Legendre transformation, Hamiltonian actian Sections 3.1.1, 3.1.2, 3.1.3
16 Phase space reduction, Poisson brackets Sections 3.2, 3.3, 3.4
17 Evolution and surfaces of section Sections 3.5, 3.6 through 3.6.2
18 Autonomous systems: Henon and Heiles Sections 3.6.3, 3.6.4
19 Exponential divergence, solar system Section 3.7
20 Liouville theorem, Poincare recurrence Sections 3.8, 3.9
21 Vector fields and form fields  
22 Poincare equations  
Phase space structure
23 Linear stability Sections 4.1, 4.2
24 Homoclinic tangle Section 4.3
25 Integrable systems Section 4.4
26 Poincare-Birkhoff theorem Section 4.5
27 Invariant curves, KAM theorem Section 4.6
Canonical transformations
28 Canonical transformations, point transforms, symplectic conditions Sections 5.1, 5.2, 5.3, 5.4
29 Mixed-variable generating functions Sections 5.6, 5.6.4
30 Time evolution is canonical Section 5.7
31 Hamilton-Jacobi equation Section 5.8
32 Lie transforms and Lie series Sections 5.9, 5.10
Perturbation theory
33 Perturbation theory with Lie series Sections 6.1 up to 6.2.1
34 Small denominators and secular terms, pendulum to higher order and many degrees of freedom Sections 6.2.1, 6.2.2, 6.3
35 Nonlinear resonances, reading the Hamiltonian, resonance overlap Sections 6.4 up to 6.4.4
36 Second-order resonances, stability of the vertical equilibrium Sections 6.4.4, 6.4.5
37 Adiabatic invariance and adiabatic chaos