Helicopter ground resonance is an unstable dynamic phenomenon which can lead to the total destruction of the aircraft during take-off or landing phases. Studies have been developed by researchers which considered a simplified mathematical model. With the goal of further comprehend the phenomenon, predictions of unstable motions are done and compared. First, Floquet's theory is applied to solve the linear equations of motion including parametric and periodic terms. Then, the multiple scales method is applied on the nonlinear model. The analyses highlight that, by keeping the nonlinear terms in the equations, other instability zones are identified.