A Constructive Method for Computing Generalized Manley-Rowe Constants of Motion (Communications in Computational Physics, 2013)
The Manley-Rowe constants of motion (MRC) are conservation laws writtenout for a dynamical system describing the time evolution of the amplitudes in resonanttriad. In this paper we extend the concept of MRC to resonance clusters of any formyielding generalized Manley-Rowe constants (gMRC) and give a constructive methodhow to compute them. We also give details of a $Mathematica$ implementation of thismethod. While MRC provide integrability of the underlying dynamical system, gMRCgenerally do not but may be used for qualitative and numerical study of dynamicalsystems describing generic resonance clusters.