MODE COMPETITION IN A SYSTEM OF 2 PARAMETRICALLY DRIVEN PENDULUMS - THE DISSIPATIVE CASE

In this paper we study the dynamics of a system of two linearly couple d, parametrically driven pendulums, subject to viscous dissipation. It is a continuation of the previous paper (E.J. Banning and J.P. van de r Weele (1995)), in which we treated the Hamiltonian case, The damping has several important consequences, For instance, the driving amplitu de now has to exceed a threshold value in order to excite non-trivial motion in the system. Furthermore, dissipative systems (can) exhibit a ttraction in phase space, making limit cycles, Arnol'd tongues and cha otic attractors a distinct possibility. We discuss these features in d etail. Another consequence of the dissipation is that it breaks the ti me-reversal symmetry of the system. This means that several, formerly distinct motions now fall within the same symmetry class and may for i nstance annihilate each other in a saddle-node bifurcation, Implicatio ns of this are encountered throughout the paper, and we shall pay spec ial attention to its effect on the interaction between two of the norm al modes of the system.