Konwersatorium im. Leopolda Infelda

In this talk I will describe the geometry associated with some very interesting nonholonomic mechanical systems.
The word `nonholonomic' means that the velocities of the systems will obey constraints -- here I will focus on examples when one has linear cosntraints on velocities. Two classes of examples will be discussed:
a) `planar robots', some of which model the movements of snakes, and b) `a disk in 3-space', which may model the behavior of a flying saucer.
I will show that in these examples the configuration spaces of the systems are equipped with rich geometric structures, which naturally correspond to certain simple Lie algebras, both classical as well as exceptional.