Abstract: The derivatives of the rotor are very important in the studies of the stability and control. Generally, the models considered in studies of the stability of the helicopter include only the flapping motion and the induced velocity with simple distribution.In this paper, the first harmonic variation of induced velocity distribution derived by Wang's generalized vortex theory is taken into account in detial, and the coupling of the first flapping-lagging bending mode of the blade elasticity is also considered.A sample calculation of a typical helicopter have been made. The influences of the induced velocity distribution and the coupling flapping-lagging on the derivatives of the rotor and the stability of the helicopter is described and drawn in detail, in particular, the derivatives of the rotor with u parameter. All the basic mechanical expressions of the hingeless rotor are presented.