MEASUREMENT AND ANALYSIS OF COMPLEX MODULATED MOTIONS IN A WEAKLY NONLINEAR-SYSTEM

The two-timing dynamics of a forced, weakly nonlinear system are consi dered. Experimental results on a roll-forced spherical pendulum verify the occurrence of slow-time, subharmonically and chaotically modulate d oscillations in a frequency band near resonance; the modulatory beha vior follows the occurrence of a Hopf bifurcation in the slow-time coo rdinates. A phase-sensitive detection method for experimentally isolat ing the slow-time behavior is described. A Lagrangian model for the pe ndulum is developed, and slow-time equations are presented. A two-thir ds power scaling law relating roll angle to the appearance of the modu lations is derived from the slow-time equations and tested with experi mental results. (C) 1998 Elsevier Science B.V.