Affine symmetry in mechanics of collective and internal modes. Part I.   Classical models
  Discussed is a model of collective and internal degrees of freedom with kinematics based on affine group and its subgroups. The main novelty in comparison with the previous attempts of this kind is that it is not only kinematics but also dynamics that is affinely-invariant. The relationship with the dynamics of integrable one-dimensional lattices is discussed. It is shown that affinely-invariant geodetic models may encode the dynamics of something like elastic vibrations. 
J. J. S{\l}awianowski, V. Kovalchuk, A. S{\l}awianowska, B.   Go{\l}ubowska, A. Martens, E. E. Ro\.zko, Z. J. Zawistowski