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COURSE: PHYS 6102 Classical Mechanics II, Spring 2013
        12:05 pm - 12:55 pm MWF Howey  S104
INSTRUCTOR: Jean Bellissard

This course will be dedicated to study special problems where Classical
Mechanics is the core of the explanation. The list of Special Problems
below is not exhaustive and might be modified before the beginning of the
semester or during the course to adjust to the need of the audience

In addition, the Graduate Students participating in this course will be
asked to choose a topic of their choice, with a strong emphasis on
Classical Mechanics, and to prepare a report about this topic which will
be presented in class during the second half of the semester.

The following list is only indicative. Since Fluid Mechanics is taught
in PHYS 4421, it will not be treated here in priority. But topics in fluid
mechanics might be re-introduced depending upon the demand of students.

1)- Completely Integrable systems. The Liouville Theorem. Lax pairs.
Symmetry groups. Some of the following examples could be treated: the
Jacobi top, the Toda lattice, solitons like in the KdV equations, the
Boussinesq equation, Kadomtsev-Petviashvili equation (the list is not
limited). Application to isospectrality (inverse scattering method) for
the Schr\"odinger equation.

2)- Differential Geometry and Classical Mechanics. Notion of tangent and
cotangent bundle. Connections form, torsion. Exterior Calculus. Group
action, moment map. Symplectic Geometry approach to Classical Mechanics.
Applications to representation of semisimple compact Lie groups

3)- Global aspects. The Poincare recurrence theorem. Concept of
ergodicity. The Birkhoff theorem. The von Neumann ergodicity. Liouville
measure. Phase space portrait. Periodic orbit. Lyapounov stability.
Concept of ellipticity, and hyperbolicity. Example of billiards. The
Aubry-mather theory and the Peierls barrier. Application to the
Frenkel-Kontorova models. Introduction to, statement and interpretation
of the KAM theorem.

4)- Mechanics of solids. Rigid solids, center of mass motion, rotation,
moment of inertia, torque. Viscoelasticity, eigenmodes distribution.
Stress and strain, plasticity, dislocation. Some more modern topics like
the STZ theory (shear transformation zones) of Langer {\em et al} might
be introduced and study, leading to the plasticity curve in metallic
glasses.

5)- Classical Field Theory. Concepts of Lagrangian and action.
Symmetries. Noether Theorem. Field equation (Euler Lagrange).
Application: the Landau mean field theory. Several examples can be
treated such as: Landau equations for ferromagnetism, Ginzburg-Landau
equations for superconductivity, the Noziere-Pines approach to Fermi
liquid theory, the distortion free energy density in liquid crystals.

6)- Constrained systems (topic to be developed further). Holonomic
constraints. Applications to robotic.
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