Title: The method of multiple scales and the perturbation-incremental method for autonomous non-linear oscillators
Authors: Ng, Kwok Tim (伍國添)
Abstract: In this report, a method of multiple scales is presented for the analysis of weakly non-linear
oscillators in the form 2 2 2 0 , d u du
u F u
dt dt
+ω =ε
, where ,
du
F u
dt is arbitrary non-linear
function of its arguments and 0 0 . The perturbation-incremental method
is an extension of the classical perturbation method to the case where λ is not necessarily
small. The method incorporates salient features from both the perturbation method and the
incremental method. Matlab is used for the perturbation-incremental method. Limit cycles
of an oscillator can be calculated to any desired degree of accuracy. The stability of a limit cycle is also considered.