The core material for this course is contained in the assigned textbook (3rd edition) through the end of Chapter 11, but we omit Special Relativity (Chapter 7) because it is covered in other courses. The material in Chapters 12 and 13 is also covered to a large extent in other courses.

The list below corresponds to all topics covered in past years when I taught this course. The numbers refer to sections in the textbook (3rd ed.). There might be a few omissions this year (if so, the list below will be updated).

Review of classical mechanics at level of introductory undergraduate physics (1-1 & 1-2).
D'Alembert's Principle and Lagrange's equations (1-3 & 1-4).
Dissipation function ( last part 1-5 ).
Applications of the Lagrangian (1-6).

Hamilton's Principle (2-1).
Calculus of variations (examples in 2-2).
Euler-Lagrange diff. eqns. (2-3).
Lagrange multipliers (parts of 2-4).
Conserved quantities and associated symmetries (2-6).

TEST I

Two-body central forces & the one-body 1-D equivalent (3-1 thru 3-3).
Classification of orbits (3-3).
Virial theorem (3-4).
Orbit shapes & Bertrand's Theorem (parts of 3-5, 3-6).
The Kepler problem (3-7 thru 3-8).

Rotations of a rigid body; matrix representation (4-1 thru 4-3).
Euler angles (4-4).
Infinitesimal rotations (4-8).
Time derivatives in rotating frames & Coriolis force (4-9 & 4-10).

Tensors (5-2).
Inertia tensor and moments of inertia (5-1 & 5-3).
Principal moments and principal axes (5-4).
Euler eqs. of motion (5-5).

Normal coords & normal modes for small oscillation (abbreviated 6-1 thru 6-3).
Linear triatomic molecule (6-4).
Forced vibrations & dissipation (6-5).

TEST II

Hamilton's EOM & conservation theorems (abbreviated 8-1 & 8-2).
Variational principles and the Hamiltonian (8-5 & 8-6).

Canonical transformations & generating functions (9-1 thru 9-3).
Symplectic formulation (abbreviated 9-4).
Poisson brackets, infinitesimal canonical transformations, & conservation (9-5 & 9-6).
Angular momentum & Poisson brackets (9-7).
Liouville's Theorem (9-9).

The Hamilton-Jacobi method; Hamilton's principal fn. & characteristic fn. (10-1 thru 10-3).
Separation of variables (10-4).

Introduction to deterministic chaos.
The logistic equation & the logistic map equation.
Graphical and algebraic approaches to map analysis.
Bifurcation diagrams and Lyapunov exponents.

FINAL EXAM

Last updated: August 2007