OBTAINING THE EQUATIONS OF MOTION FOR PARAMETRICALLY COUPLED OSCILLATORS OR WAVES.
HARVARD UNIV CAMBRIDGE MASS CRUFT LAB
Pagination or Media Count:
By employing appropriately defined mormal mode amplitudes as variables, one can cast the equations of motion for any parametric system into a general coupledmode form, where this form depends on the number of frequency components present and on the order of the nonlinearities present, but not on any other details of the particular physical system. A simple procedure, based on a Hamiltonian approach, is given, by which one may obtain the general form of the equations of motion for any multifrequency parametric system, including parametrically coupled oscillators with growth in time, parametrically coupled running waves with growth in both time and distance. The general equations obtained by this procedure are useful for pedagogic purposes and general discussions as a means of either avoiding the need for, or checking the results of, more complicated derivations on specific physical systems as the starting point for quantizing the parametric system and as a means of proving the Manley-Rowe relations, which emerge very directly from the resulting general equations. Author