It will always rotate in the same direction. It will run on square wave
but hotter than normal and it will kickback into the drivers something
terrific. It needs a full wave voltage to work (can't have dc through it
although some motors can). This means transformer or H bridge or 1/2 H
drive. The usual scheme is doubler rectifier from ac into two series
capacitors and push-pull driver driving the motor between the pushpull
output and the center point of the capacitors. As I have said, if the
waveform is not sinus there will be major kickback issues. The starting
current can be scary (depending on construction).

You can always replace a synchronous motor with a stepper which is easier
to drive (but won't do 3000 rpm easily). A stepper driven with 2-phase
drive and a better driver IC will likely outperform the synchronous motor
in all respects except cost and weight.

Peter

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