Polarization effects due to the mutual influence of trajectory parameters and polarization

In the geometric optics approximation, we comparatively analyze the polarization effects resulting from the influence of polarization on the beam trajectory. We show that the beam trajectory equations describing the optical Magnus effect that are obtained from the canonical Hamilton equations, Fermat principle, and truncated vector wave equations give the same result, coincident with the result in the mode approach. We explain the reasons underlying the previously derived results.