Same as other 3P systems, just a different voltage.
Is it that you have trouble with 3P in general, or only with 3P and 110V at the same time ?
In general, a motor doesn't care whether a 1P supply is split phase, one end earthed, or any other combination. All it cares about is having an AC voktage between 2 wires.
Consider this. You are presented with 2 wires and gave no earth reference. You can measure the voltage between the wires - but you don't know much else.
Is it ungrounded - i.e. a floating supply like you'd get from a shaver socket ?
Is it 110V with one end earthed ?
Is it 55-0-55 with the centre tap earthed (technically split phase) ?
Is it two legs of a 3P supply (of which, there are different ways of earthing, or not, part of the supply) ?
As to what people call it, there is "much confysion" - and even people who should know better can be sloppy with terminology.
In particular, with a 55-0-55 supply, what it us depends to a certain extent on how many wires you have. With 2 wires it's single phase, if you have access to the centre tap then it's split phase. With a split phase, if you connect across the two lines (and ignore the centre tap "neutral"), then that's single phase for that connection.
