  It's pointed out that the treatment of the resonant electromagnetic
perturbation with the Lie transform method adopted in the gyrokinetic theory
generates some nonphysical terms in the trajectory equations. By utilizing a
modified application of this transform method, the resonant terms in the
trajectory equations satisfying each resonant condition are found out up to the
second harmonic resonance. Through separating the fast-dynamic terms from the
slow-dynamic ones, the slow-dynamic trajectory equations including the resonant
terms are derived for various resonant conditions. The slow-dynamic evolution
equation of gyroangle reveals that the real gyrating frequency of the charged
particle around the magnetic field line under driving by the resonant wave has
a shift from the cyclotron frequency without the wave driving. To study the
effect caused by the frequency shift, a simple example for the
fundamental-frequency cyclotron resonance is presented.
