SCIENTIFIC EVENTS AND ACTIVITIES
|July 28, 2014|
Geometry and Control of Coupled Structures
The Institute Director, Jerrold E. Marsden will present a series of three lectures
Sunday, March 8 - Tuesday, March 10, 1992
This series is intended for graduate students and others with an interest in an introduction to the geometry and control of coupled rigid bodies.
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.
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.
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.