Rotary phase converters give very good power but the initial cost is high and are costly to run (low efficiency) and since they are rotational machinery, will not last forever. Three phase produced by an idler motor (twice as large in hp than the motor to be operated off of the circuit) either with a pull start (a dangerous thing to do, but the idea is to get the motor spinning and then supply power) or with a starting capacitor (static phase converter) is a less expensive method of producing three phase power. However the three phase isn't perfect with an idler motor (still have legs 180 degrees apart, not 120 degrees), and the third phase is somewhere in between the 180 degrees phase angle. The third leg is usually more than 10 percent less in voltage to ground than the two supplying legs. This can be helped with capacitors, but then again for this to work correctly, the problem will become load dependent.
Variable frequency drives can be employed and most will run on single phase to supply a three phase motor with the added ability to reverse the motor and vary the output speed. They are more energy efficient in doing this compared to the other two methods above, but there are some important considerations. The drives must be de-rated in horsepower. Many people suggest that a de-rating of 2/3, however it is safer to assume a factor of 1/2 de-rating. That means that the drive will need to be twice the horsepower capacity of the motor it will run. Also, the output of the motor will need to be de-rated as well. I know this from long experience and is a true and applicable rule of thumb even if the motor and drive are supplied by a perfect three phase system. Typically a motor will have 75% the acual output on a VFD at 60 Hz than a good old sine wave from the power company. The reason is due to the chopping of the output of the drive into transients that cannot be effectively used by the motor. To put it another way, the VFD output is very noisy and little resembles a nice sine wave. So if your saw was running just fine on a full voltage starter, you may experience that the saw will not be able to handle the same cuts with the same feeds and speeds when operated on a VFD. The output of a VFD is very spikey due to the high speed switching of the IGBPT's and capacitance of the wires to the motor. This effect gets worse as the wire runs get longer (more capacitance). One way to help this is to use VFD rated cable, but this stuff is typically very expensive and more than the cost of THHN in conduit. Another way is to use load reactors, but they should be placed next to the motor which nobody ever does. So be prepared to de-rate the actual power output of the motor on a VFD as well. This being the case, then that also means that the VFD should be increased in HP capacity by another step. As an example, if I had a critical motor, say a three phase coolant pump, that is rated 1/2 hp, and it was running in my shop which is supplied by single phase and I was running it on a VFD to supply the three phase, I would probably end up replacing the motor with a 1 or 1-1/2 hp motor, and my drive would be at least a 3 hp rated VFD to handle this situation. Mind you that a 3 hp VFD is stil rather small.
Most state of the art VFD's can be programmed for constant horsepower, constant torque, and V/Hz operation. It doesn't hurt to experiment to see how your machine operates with different settings and that the VFD will display output current and voltage (good things to know). Most important thing is to keep a check on motor heating. It is best to keep the carrier frequency low as this will send less spikes to the motor, which will eventually degrade the insulation, but the motor will be noisier with a high pitch whine in operation. It is best to run a motor on a VFD which is rated for VFD operation especially at the lower output frequencies. This isn't always necessary, but don't expect years of operation from that motor. However, I did run a 1931 three phase motor on a lathe for many years on a VFD without any issues. But I suppose they really knew how to make a good motor back in 1931.