All readings are taken from the course textbook:
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).
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 |