MODE COMPETITION IN A SYSTEM OF 2 PARAMETRICALLY DRIVEN PENDULUMS WITH NONLINEAR COUPLING

This paper is part three in a series on the dynamics of two coupled, p arametrically driven pendulums, In the previous parts Banning and van der Weele (1995) and Banning et al. (1997) studied the case of linear coupling; the present paper deals with the changes brought on by the i nclusion of a nonlinear (third-order) term in the coupling. Special at tention will be given to the phenomenon of mode competition. The nonli near coupling is seen to introduce a new kind of threshold into the sy stem, namely a lower limit to the frequency at which certain motions c an exist. Another consequence is that the mode interaction between 1 a lpha and 2 beta (two of the normal motions of the system) is less dege nerate, causing the intermediary mixed motion known as MP to manifest itself more strongly.