Single phase variable control motors?

Hi, I am trying to find an electrical hoist, which has variable speed, single phase motors. I am unable to find any. Is there a technical reason why? Or would it be a business reason? Any insight?
Thanks.

Dear P-GPS:
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Single phase motors are fractional to small integer horsepower. You will need VFD-rated motor windings, and make sure that you do not overspeed the winding mechanism (so don't run the mechanism over 60 Hz, for example).
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Small market, you are going damned slow anyway so why worry about slower, the single phase inverter is at least 2x more expensive than the three-phase version for the same motor power, control logic for reversing the motor is orders of magnitude more complex, stuff like that.
I suggest you find a vendor that offers hoists with less than 5 hp drive motors, and single phase power is probably an expensive option.
David A. Smith

Hi, I did not get you in some of your statements
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What does this mean?
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Doesn't a speed controller limit the frequency to 60Hz, when connected to a 60Hz main?
Even if the cost of a single phase motor is 2x that of a 3-phase motor, we would like to get it. Are there any vendors who sell single phase variable motors?
Thanks.
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Dear P-GPS:
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They are small motors. < 5hp.
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No. You can obtain VFDs that will overspeed by 20% or more, with modifications they even run ozone generators at thousands of hertz.
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For < 5hp, or over 4000 volts, you can get them. If you wanted to pay 100x, you could get someone to make you one.
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The motors are not variable, the drive is. And switching it from "raise" to "lower" is much more complex than with a three phase motor, and requires a whole 'nother control system.
David A. Smith