Models for Small-Scale Structure on Cosmic Strings: I. Mathematical
  Formalism
  We describe the formalism of a quantitative analytic model for the evolution
of realistic wiggly (as opposed to Goto-Nambu) cosmic strings. The model is
particularly suited for describing the evolution of small-scale structure on
string networks. We discuss model solutions in the extreme limit where the
wiggles make up a high fraction of the total energy of the string network
(which physically corresponds to the tensionless limit) and also provide a
brief discussion of the opposite (linear) limit where wiggles are a small
fraction of the total energy. A companion paper will discuss the detailed
modelling and scaling behavior of the small-scale wiggles in the general model,
together with a basic comparison with numerical simulations.
