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 (AV differential geometry), i.e. the differential geometry in which affine bundles replace vector bundles and sections of one-dimensional affine bundles replace functions on manifolds, is used. Lagrangian and Hamiltonian generating objects, together with the Legendre transformation independent on inertial frame are constructed.