Use GoHz frequency converter in motor. Rotor is of special made. Stator winding is designed to maintain 3-phase and use a capacitor in between two phase and output will be 3-phase. We had designed in my previous company such a 1-phase to 3-phase frequency converter. These converter are used in locomotives.
There are a lot of controller for 60Hz to 50Hz frequency converter with which you can easily get a voltage down to 110V; then you can get in addition the 120V with a simple linear converter starting from the 110V. With 100 mA you have to consider a dissipation of (15-3.3) *0.1 = 1.17W. Attention that without transformer you are not in any case isolated from the power supply. If its a GoHz frequency converter whose nameplate indicates three phase. Then its possible to change from 480V 60Hz to 400V 50Hz. But if the plate indicates single phase I don't think its possible based on the 110V 60Hz to 220V 50Hz converting.
Single phase 60Hz to 50Hz frequency converter can be useful only in domestic or in isolated environments. Anyway, besides limited scope, there are limitations of power. The efficiency is too low for extended uses. Can only be an emergency solution. From the simple capacitor to sophisticated frequency converters performance increase, suitable the price. Technical efficiency in opposition to financial. Are usually more handy three phase power sources. We think by relieving and more researches any impossibility can be possible and that note I consider the theoretically aspect of 50Hz to 60Hz frequency converter example Single Phase to be rectified to DC, the output DC to be converted / inverted to 3-Phase AC.
Static frequency converters have been used to accept 230 volt single phase and will output 3 phase but need to be derated for the higher input phase currents. You statement does not provide any parameters such as voltage/capacity/application that would help in pointing towards a potential solution for converting 120V 60Hz to 230V 50Hz.
You will need to know the power or horsepower rating of the motor in order to determine the correct capacitors for the frequency converter 60Hz to 50Hz. This is low cost & basic. It may cause the motor to get a bit hot due to poor phase balancing and so may restrict the power you can get out of the motor.