Exact Description of Rotational Waves in an Elastic Solid
arXiv:0908.3232 · doi:10.1007/s00006-010-0249-1
Abstract
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.
9 pages; Added references in revision