Abstract The dynamic study of rotors is usually performed under a number of assumptions, namely small displacements and rotations, small unbalance and constant angular velocity. The latter assumption can be substituted by a known time history of the spin speed. The present paper develops a general non-linear model which can be used to study the rotordynamic behaviour of both fixed and free rotors without resorting to the mentioned assumptions and compares the results obtained from a number of non-linear numerical simulations with those computed through the usual linearized approach. It is so possible to verify that the validity of the rotordynamic models extends to situations in which fairly large unbalances and whirling motions are present and, above all, it is shown that the doubts forwarded about the application of a model which is based on constant spin speed to the case of free rotors in which the angular momentum is constant have no ground. Rotordynamic models can thus be used to study the stability in the small of spinning spacecrafts and the insight obtained from the study of rotors is useful to understand their attitude dynamics and its interactions with the vibration dynamics.