AV-differential geometry and Newtonian mechanics
  A frame independent formulation of analytical mechanics in the Newtonian space-time is presented The differential geometry of affine values i.e., the differential geometry in which affine bundles replace vector bundles and sections of one dimensional affine bundles replace functions on manifolds, is uded. Lagragian and hamiltonian generating objects, together with the Legendre transformation independent on inertial frame are constructed. 
Katarzyna Grabowska, Pawel Urbanski