2 EXTENSIONS TO KANES METHOD FOR SIMPLIFYING EQUATION DERIVATION

Two extensions to Kane's method are presented. First, a strategy is pr oposed for using Kane's method to derive dynamical equations for syste ms with flexible components. During the derivation, each flexible comp onent of the system is represented by a ''surrogate element'' which ca ptures the response characteristics of that component. The derivation proceeds essentially as if each surrogate element were a rigid body. A pplication of Kane's method yields a set of simultaneous differential equations which can then be transformed to be the exact, partial diffe rential equations for the original flexible system. Use of this strate gy (as opposed to an assumed mode solution strategy) greatly facilitat es generation of exact equations using Kane's method. In the second pa rt, a general method for generating simpler equations of motion for an y system while using Kane's method is demonstrated with examples. A si mple row-reduction is applied to the partial velocity table producing equations with fewer terms. In addition, the row-reduction can lead to a change in choice of generalized speeds that further simplifies the equations of motion.