Jim Wilson wrote:

Thanks for all the responses.

A flywheel would reduce, not increase, the idler's ability to respond to
load changes. When the electrical load on the idler increases, the
idler's rate of rotation falls (I.e., the slip increases). This raises
the current draw from the single phase source. The higher winding current
increases the strength of the rotating magnetic field in the idler, which
pushes the generated third leg voltage up. The upshot of all this is that
the response rate of the third leg voltage to electrical load changes is
inversely related to the inertia of the idler's armature.

I'm not sure about this. Yes, it will take longer for the rotor's speed
to fall, but surely the stored energy will be dissipated by driving
extra current through the load?

Best wishes,

Chris