Self-interaction of an arbitrary moving dislocation

The action functional for a linear elastic medium with dislocations is given. equations of motion following from this reproduce the Peach-K\"{o}hler and Lorentzian forces experienced by dislocations. explicit expressions singular finite parts self-force acting on curved dislocation are derived in framework theory elasticity an isotropic medium. velocity assumed to be arbitrary but less than shear wave velocity. slow speed near-sonic motions investigated. In limit, expression leading contribution obtained. case slowly moving dislocations, effective present paper known results.