Some aspects of affine motion and nonholonomic constraints. Two ways to describe homogeneously deformable bodies

Abstract

This paper has been inspired by ideas presented by V. V. Kozlov in his works [19,20]. In this paper our goal is to carry out a thorough analysis of some geometric problems of the dynamics of affinely-rigid bodies. We present two ways to describe this case: the classical dynamical d'Alembert and variational, i.e., vakonomic one. So far, we can see that they give quite different results. The vakonomic model from the mathematical point of view seems to be more elegant. The similar problems were examined by Jóźwikowski and W. Respondek in their paper [16].