A heavy top drifting in space
No. 74, 1973
(Hamiltonian mechanics, symplectic geometry)
India ink, pencil, and oil on paper, 30.5x42.5 cm.
A rigid body rapidly spins in space, like a top on its axis. Thus a gyroscope is created, which has the remarkable property of maintaining its position in space and holding to a course of motion, despite the twists and turns of the vessel on which it is seated. For this reason, gyroscopes play a critical role in navigating aircrafts and rockets. To study their equations of motion, mathematicians appeal to the theory of differential equations, symplectic geometry, algebra, and topology. Of interest too is the case where the rotating object is not symmetrical and its motion is chaotic. It may somersault wildly in space, and to understand its motion involves some very intricate mathematics.
