Complex equations of motion for a body under gravitational influence by using a nine-parameter space-time bundle with the structural group SO(3,C)

We give equations of motion of a body under gravitational influence using a model which employs nonlinear connection adapted to 3+3+3-dimensional bundle. It is analogous to the corresponding 3+1 model with nonlinear connection in Minkowski spacetime. The equations of motion are simple complex equations whose real part gives the equations of motion previously obtained in the 3+1 model with nonlinear connection in Minkowski spacetime. They lead to the same predictions as the General Relativity, which are experimentally verified. The imaginary part of the equations of motion gives the total precession of a gyroscope (geodetic precession and frame dragging). The complex equations of motion can be used also in electrodynamics. In this case, the imaginary part corresponds to the Lorentz force, while the real part leads to the angular velocity of an electron in a magnetic field. It is obtained Ω→=emcH→ (if E→=0), which fits well with the observations.