3.2.1 State equation for dependent inertial masses J and J Develop a single state equation for the dependent inertial masses J and J2. The easiest way in this case would be to reflect J to the right-side of the gears and make an equivalent system J as illustrated in Fig. 6a. T(t) w(t) J E XXXX D T J E k03 direction of rotation ' k , JEW2 E (a) Mass/gear equivalent model for J1, J2, and the connecting gears DEW2 (b) Free-body diagram for JE Figure 6: Mass/gear equivalent model JE and its free-body diagram. Some useful equations for gears are TN2 TN1 = ONL 0N2 = N2 N (24) (t) N 1 rigid J 2 XXXX k J 3 D XXXX D 2 3 fem (t)) km R L 0000 i Generator k Motor rigid Massless Drum x(t) M Gravity, g 0000 x(t) M Figure 5: Rotational-translational electromechanical system. B 1 Analyzing the model given in Fig. 5, it should be clear that a good choice for the state variables are . w2: for the angular velocity of J2 for the dependent inertial masses J and J 0s = 02-03: for the angular twist of the torsional spring with spring constant k S w3: for the angular velocity of the inertial mass J3 i: for the current through the inductor v1: for the velocity of mass M x = x1 = x2: for the translational compression of spring with spring constant k2 v2: for the velocity of mass M2