It is easy to run a 3 phase motor on single phase as long as it is under 3 horsepower. We do it all the time using a VFD (Variable frequency drive). It takes your single phase power, converts it into DC and smooths it with a capacitor bank, and then uses IGBT's (or another type of solid state switch) to make a new 3 phase waveform. You can go over 3 horsepower, but they require derating, and only certain drives will allow you to do it. Here are the drives I normally use:
https://www.automationdirect.com/adc/Shopping/Catalog/Motor_Controls/Drives/DURApulse_-_GS3_(230_-z-_460_VAC_Sensorless_Vector_Control)/DURApulse_-_GS3_Drive_Units_(230_-z-_460_VAC_SLV)#Input_ms="230+VAC+1/3+Phase"&start=0
$250-350 isn't too bad for what they will do. You can also vary the motor speed if you wanted.
If you don't know what you are doing, then don't attempt to hook one of these up on your own! Also, don't try to use one without configuring it properly!