We present general solutions to the equations of motion for a superconducting
relativistic chiral string that satisfy the unit magnitude constraint in terms
of products of rotations. From this result we show how to construct a general
family of odd harmonic superconducting chiral loops. We further generalise the
product of rotations to an arbitrary number of dimensions.Comment: 6 pages, RevTex. Replaced with version accepted for publication in J.
Math. Phy