In order to determine the dynamic response of a complex rotor system to imbalance

a new approach is developed

based on the state equation and transition matrix of motion of a rotor.By means of this method

the exact solution of rotor vibration response can be directly obtained without any information about its modes in advance.Furthermore

as the transition matrix can be transformed into a transfer matrix

so this approach can be combined with transfer-matrix method

and the dynamic response of a complex rotor system to imbalance can be easily computed.A numerical example shows

that this approach is an effective and short-cut method.