Rolling and sliding
No. 188, 1976
(Nonholonomic mechanics)
India ink and pencil on paper, 41x62 cm.
On an icy plane, disks skid around aimlessly—some bouncing, some sliding, others colliding with each other. In fact when objects like records, ice skates, or other kinds of blades slide along, they demonstrate nonholonomic systems, or systems with nonholonomic constraints. A classical example: when we ice skate, the blades of our skates cannot slide sideways. Mathematically speaking, this means that a differential equation corresponding to a nonintegrable distribution serves as a constraint. This picture investigates the motions of sharpened disks as they slide along, creating a mechanical system as well as some truly nontrivial mathematical problems. In this case, we can create a nonholonomic system from a holonomic system by attaching semicircular blades to a rigid body revolving in space, sliding along the inner surface of a rigid sphere, inside of which we place a spinning top. Each blade like this imposes a nonholonomic constraint on the original system.
