Ingarden mechanical systems with special external forces

In the present paper we study a remarcable particular case of Finslerian mechanical system, called Ingarden mechanical system. This is defined by a 4-uple ∑_IFⁿ = (M, F², N, Fe) where M is the configuration space, Fⁿ = (M, F, (x, y)) = (M, α, (x, y) + β (x, y)) is an Ingarden space, N is the Lorentz nonlinear connection and are the external forces.

One associates to this system ∑_IFⁿ a semispray S, or a dinamical system on the velocity space TM. We write the generalized Maxwell equations for the electromagnetic fields of ∑_IFⁿ.