Linear frames in manifolds, riemannian structures and description of internal degrees of freedom

Discussed is affine model of internal degrees of freedom, i.e. infinitesimal Affnely rigid body in a manifold. The treatment is nonrelativistic and classical. The special stress is laid on geodetic models and invariance classification of a priori possible kinetic energies. Geometrically this is equivalent to deriving natural Riemannian structures in the bundle of linear frames from some geometry on the base manifold (affine connection, metric). It turns out that the general structure of dynamical balance laws resembles that derived in general relativity for the pole-dipole particle. Linear momentum and (affine) spin are coupled to the torsion and curvature tensors.