Fields Institute - Geometry and Control of Coupled Structures - 1992


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		December 26, 2024
			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. 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.