  We investigate the dynamics of gravitational field and particles in a
generalized framework of a Lorentz tangent bundle. By variating an appropriate
action for each case, we obtain generalized forms of paths and generalized
field equations for a Sasaki type metric. We show that Stokes theorem is
modified with respect to general relativity due to local anisotropy and the
presence of a nonlinear connection which induces an adapted basis in our space.
