This series is intended for graduate students and others with an interest in an introduction to the geometry and control of coupled rigid bodies.

Lecture 1: Geometric mechanics and the mechanical connection
Lecture 2: Stability and the separation of internal and rotational modes
Lecture 3: Control and Stabilization

Abstracts

Lecture 1: Geometric mechanics and the mechanical connection

A survey of topics in mechanics, including the cotangent bundle reduction theorem and geometric phases. The mechanical connection and how to complute it for examples like the double spherical pendulum and the ozone molecule. Montgomery's formula for the rigid body phase.

Lecture 2: Stability and the separation of internal and rotational modes

The energy momentum method and the separation of modes for a stability and bifurcation analysis of uniformly rotating states. The double spherical pendulum and the heavy top are used as illustrations. The blowing up of singularities at symmetric states and the role of dicrete symmetries.

Lecture 3: Control and Stabilization

How to use Lie-Poisson geometry to study the control and stabilization of rigid bodies with internal rotors. The Wilczek-Shapere-Montgomery result on optimal control and the gauge theory of mechanics.

There will be a concurrent workshop on The Falling Cat and Related Problems.