  Conventional descriptions of transverse waves in an elastic solid are limited
by an assumption of infinitesimally small gradients of rotation. By assuming a
linear response to variations in orientation, we derive an exact description of
a restricted class of rotational waves in an ideal isotropic elastic solid. The
result is a nonlinear equation expressed in terms of Dirac bispinors. This
result provides a simple classical interpretation of relativistic quantum
mechanical dynamics. We construct a Lagrangian of the form L=-E+U+K=0, where E
is the total energy, U is the potential energy, and K is the kinetic energy.
