Geometry and Classical Mechanics

Jerry Marsden
(Department of Control & Dynamical Systems, Cal Tech)

Saturday, February 8, 1997
9:30 AM

One of the many problems that control theory addresses is that of feedback stabilization. A simple example illustrating what is meant is how humans learn to balance (that is, stabilize) when walking, riding bicycles, or to balance inverted broomsticks, or whirling a lasso. Related examples are the problem of stabilizing a spinning satellite and the reorientation problem for a springboard diver. This talk presents a general stabilization technique introduced by Bloch, Krishnaprasad, Marsden and Sanchez in the context of a rigid body with internal rotors. This technique is now known to result from a general Kaluza-Klein type of construction, familiar to geometers and physicists. Other examples, such as stabilizing an inverted pendulum on a cart, the dynamics of an underwater vehicle and the motion of a double spherical pendulum will also be discussed.

Back to Winter 1997 meeting of the PNGS.

Suggestions or corrections to

Jack Lee <>.