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Planetary gears are widely used in the transmissions of helicopters, automobiles, aircraft engines, etc. They have substantial advantages such as compactness and a large torque-to-weight ratio. In this work, a plane model of a planetary gear was investigated. The energetic Lagrange formulation was used to recover the equations of motion of the system. A modal analysis was performed, and the influence of gyroscopic effect in particular was scrutinized. The dynamic response was computed by an iterative spectral method. The excitation is induced by time-varying the gearmesh stiffness. The cases of a healthy planetary gear and one with the presence of eccentricity and profile error were compared. The influence on the transmission ratio was also studied.