Forced Self-Sustained Oscillator

Apteronotus

Hi,

I'm reading about self-sustained oscillators under the influence of harmonic forcing. The topic is introduced by studying the system in a new reference frame; one which rotates in the same direction with the frequency of the of the external force.

In this new reference frame, the oscillating force is represented by a constant vector, acting at some angle. (see pg 48 Synchronization)

At first glance, I thought the concept was trivial, but now I'm having a very hard time understanding why this would be so. Can anyone shed some light on this topic?

Thanks

ps. consider this...

--A stationary point in this reference frame is one which is oscillating in the original reference frame, with the same frequency as the force.

--The force on such a point is then said to be constant.

--However, to my understanding, the force in the original reference frame varies with time, indifferent of the objects position!!