DNA can be viewed as a semiflexible polymer, and represented at a coarse scale as a continuous helical elastic rod. In this talk, methods from the theory of Lie groups are used to analyze equilibrium conformations of helical rod models of DNA with end constraints. When the ends of a segment of DNA are free to move, the resulting cloud of reference frames visited by the distal end of the segment relative to the proximal end can be characterized as a probability density function on the Euclidean motion group. The relationship between this pdf and the stiffness parameters of the helical rod model is derived using methods of noncommutative harmonic analysis.