Group invariance in nonlinear motion of rods and strings

Abstract

The role of group invariance in nonlinear motion of strings and rods is discussed. Problems relating to propagation of waves in rods with nonlinear elastic, elastoplastic, and viscoplastic materials are considered. A classification of linear and nonlinear equations of motion of rods and strings is given by the study of their invariance under inspectional groups, namely, dimensional, translational, and spiral groups of transformations.