Based on the angular velocity transformation matrix, the paper develops the differential motion equation BKTJBKdωIK/dt=BKTM for a planetary transmission, which is a linearly constrained system. Although the degrees-of-freedom of the system is varying during shift process, the angular velocity transformation matrix BK, whose entries are constans, is only related to engaged clutches and BK can be easily derived from a constant matrix BF by linear transformation. Based on this theory, a computer simulation program of dynamic analysis of a planetary transmission is written, which provides a perfect means for analysis of dynamic behaviour of a transmission at any shifting transients. As an illustration, that of an Allison-WT transmission from 3rd speed to 4th speed is simulated.