Geometry and Classical Mechanics
Saturday, February 8, 1997
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
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.
Winter 1997 meeting of the PNGS.
Suggestions or corrections to Jack Lee <firstname.lastname@example.org>.