  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 J\`o\'zwikowski and W. Respondek
in their paper [16]
