Don sez:
" Sure it does. With the idler spinning, a voltage is generated in
the third leg that is in quadrature to line voltage, even if there are
no capacitors anywhere. Transformer action can not produce a
quadrature voltage so it must be (and is) generated by the rotating
rotor field -- which always is in quadrature with the stator field."

I'm not sure what you mean, Don. You said "Transformer action can not
produce a quadrature voltage so it must be (and is) generated by the
rotating rotor field -- which always is in quadrature with the stator
field".

Firstly, I don't understand why the issue must be complicated by bringing
the rotor field into the picture. It is well known the stator field and
rotor field are more or less locked into rotation at the same speed, but it
is incongruous to speculate the rotor field is solely responsible for the
stator field's third leg voltage. Remember we are essentially talking about
a single phase motor here with an open coil connected to the center point of
the line-fed main winding. I respectfully submit the third leg voltage is
not in quatrature with line voltage. The only way for that to be a true
statement would be in the special case of a precise amount of capacitance
connected from one line side to the end of the 3rd leg coil; an amount of
capacitance (start cap if you will) necessary to achieve an exact 90 degree
phase shift between line voltage and the 3rd. leg.

Bob Swinney