Finsler geometry in relational approach in physics
It is shown, that several problems occurring in classical geometrodynamics rely on the fact that the plane curves of revolution which describe the spiral galaxies, the Tully-Fisher law, and several other problems can be removed if considering the equivalence principle, with the modified expression of the metric, within the Hilbert-Einstein action. This leads to generalized equations of geodesics, and further to equations of the gravitational field which contains not only the Newtonian term. This approach contains all the results of classical geometrodynamics. The connections between the obtained results and both the consequences of the Lenze-Tirring approach, and possible cosmological consequences, are investigated