The new field of computer graphics can be used for investigating phenemona arising in the very old field of classical mechanics. Many of the problems in classical mechanics can seen in 4-dimensional phase space, and their solutions are 3-dimension constant energy surfaces. The behavior of the solutions is often determined by the topology of the constant energy surfaces, but visualization and analysis of these surfaces was exceedingly difficult before the advent of computer graphics.
The first section of this paper discusses the topology of a well understood class of integrable Hamiltonian systems. Then we examine the class of quadratic Hamiltonians in four dimensions. We have included two computer-animated color films of linear Hamiltonian systems.