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Topology and Mechanics with Computer Graphics

by Huseyin Kocak, Frederic Bisshopp,

Thomas F. Banchoff, and David Laidlaw

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.