The powertrain multibody model of a clutchless AMT is significantly simplified from an equivalent AMT or similar transmission. It relies on the synchronizer mechanism and precise motor control to realize gearshifts. As such, major components, such as flywheel, primary friction clutches, and torsional dampers, are not present in the transmission, simplifying the overall system. The multibody model is shown in Fig. 3, and equations of motion are derived in Eqs. (3)–(9). For the model, *J*_{1} represents the motor rotor and is coupled to the DC motor model per Eqs. (1) and (2), *J*_{2}_{a} is the synchronizer equivalent inertia, *J*_{eq} is the equivalent transmission inertia, *J*_{4} and *J*_{6} represent wheel hubs, and *J*_{5} and *J*_{7} are the equivalent vehicle inertias. Input torques acting on the system are (*T*_{EM}) electric machine torque, (*T*_{SYN}) synchronizer cone clutch torque, and (*T*_{V}) vehicle resistance torque. Accordingly, each inertia element has a corresponding degree-of-freedom. *θ*_{n} represents rotational displacement corresponding to the *n*th degree-of-freedom, and its two time derivatives represent velocity and acceleration. Subscript *n* corresponds to each specific degree-of-freedom (i.e., 1, 2*a*, eq, 4, 5, 6, or 7) in Fig. 3. *i* represents the gear ratios, subscript 1 represents any of the given transmission ratios, and 2 is the final drive ratio