  We examine the conformations of a model for a short segment of closed DNA.
The molecule is represented as a cylindrically symmetric elastic rod with a
constraint corresponding to a specification of the linking number. We obtain
analytic expressions leading to the spatial configuration of a family of
solutions representing distortions that interpolate between the circular form
of DNA and a figure-eight form that represents the onset of interwinding. We
are also able to generate knotted loops. We suggest ways to use our approach to
produce other configurations relevant to studies of DNA structure. The
stability of the distorted configurations is assessed, along with the effects
of fluctuations on the free energy of the various configurations.
