  We reconsider the periodically driven two level system and especially the
Rabi problem with linear polarization. The Floquet theory of this problem can
be reduced to its classical limit, i.e., to the investigation of periodic
solutions of the classical Hamiltonian equations of motion in the Bloch sphere.
The quasienergy is essentially the action integral over one period and the
resonance condition due to J.H. Shirley is shown to be equivalent to the
vanishing of the time average of a certain component of the classical solution.
This geometrical approach is applied to obtain analytical approximations to
physical quantities of the Rabi problem with linear polarization as well as
asymptotic formulas for various limit cases.
