The Mechanics of the Homogeneously‐Deformable Body. Dynamical Models with High Symmetries

Abstract

Abstract We investigate here some high‐symmetric isotropic models in the theory of nonlinear vibrations of systems with degrees of freedom governed by a linear group (affinely‐rigid bodies undergoing gyroscopic rotations and homogeneous deformations). The methods developed here can be applied both to microscopic (molecular, or even nuclear) and macroscopic elastic and visco‐elastic problems. In particular, our models can be used in the theory of generalized, micromorphic continua consisting of infinitesimal, homogeneously‐deformable grains.