Integration of the Simplified Equation of Motion

Abstract

With the assumptions introduced in the preceding section the motion of a single axis lumped inertia drive is described by a first order differential equation (Fig. 3.1)

$$J\frac{{d\omega }}{{dt}} = {{m}_{M}}\left( {\omega ,{\mkern 1mu} {\mkern 1mu} t} \right) - {{m}_{L}}\left( {\omega ,{\mkern 1mu} {\mkern 1mu} t} \right) = {{m}_{a}}\left( {\omega ,{\mkern 1mu} {\mkern 1mu} t} \right)$$

((3.1))

, which upon integration yields the mechanical transients. Several options are available for performing the integration.