Mathematical Classical Mechanics
This course is intended to complement classical mechanics
courses like Physics 206 in the sense that the physical background
will be developed but the emphasis will be on the resulting mathematical
analysis. Students should already have some experience with rigorous mathematics
(like Math 320 and 321) and with classical mechanics (like Physics 206)
although these prerequisites may be waived at the discretion of the instructor.
V. I. Arnold, Mathematical Methods of Classical Mechanics,
I will post all handouts, problem sets, etc. on the web
G. Gallavotti, The Elements of Mechanics.
H. Goldstein, Classical Mechanics.
The principles of relativity and determinacy, the gallilean group,
Examples: the harmonic oscillator, pendulum and central fields
An introduction to phase space, conservation of energy, momentum and
Constraint Free Lagrangian Mechanics:
Variational problems and the Euler-Lagrange equation
The lagrangian and Hamilton's principle of least action
The hamiltonian and Hamilton's equations
Poincaré recurrence theorem
Lagrangian Mechanics on Manifolds:
The introduction of manifolds through constraints
Differentiable manifolds and tangent bundles
Symmetry and Conservation laws: Noether's theorem
Exterior algebra, differential forms on manifolds, exterior
differentiation, vector analysis
Chains, integration of differential forms
There will be weekly problem sets accounting for about 50% of the final mark.
The final exam will account for about 50% of the final mark.
Grades will probably be scaled.
The final examination will be strictly
closed book: no formula sheets or calculators will be allowed.
There is no supplemental examination in this course.
Late homework assignments normally receive a grade of 0.
Missing a homework normally results in a mark of 0.
Exceptions may be granted in two cases: prior consent of the instructor
or a medical emergency.