  Low-harmonic formulas for closed relativistic strings are given. General
parametrizations are presented for the addition of second- and third-harmonic
waves to the fundamental wave. The method of determination of the
parametrizations is based upon a product representation found for the finite
Fourier series of string motion in which the constraints are automatically
satisfied. The construction of strings with kinks is discussed, including
examples. A procedure is laid out for the representation of kinks that arise
from self-intersection, and subsequent intercommutation, for harmonically
parametrized cosmic strings.
