4st genset is 3 phase with full sine inverter to 240v 50hz 650w +12vdc 80w,
i cannot pull start it without pain/injury.

want to patch in 12v/220v 50hz 300w /600wp approx sine wave inverter [for startup] to one phase, with a phase shift capacitor to another phase to get correct rotation direction, a la brushless washing machine motors. start current should be brief, capacitor to be salvaged from similar power brushless washer motor, if not new. f socket to startup inverter, pref weatherproof capped. in output mode, what does capacitor do if still connected? value unknown.
do not know if genset is star or delta setup, so which is likely, and how does that affect proposal? if star, imbalanced phases will i need access to central node?
inverter will be permanently integrated into genset package or external plugin with jump battery.
need to keep mass down, and simple operation. a double male plugged cable may provide start power and plugin to house gpo iff mains fail AND house etc isolated from mains?

 

For this to work, You are going to have to have a proper Battery-Powered 3-Phase-Inverter that has
the capability to smoothly "ramp-up" the speed of the Generator.

A fixed Frequency Inverter is going to try to spin the Generator at ~3600 RPM ..... INSTANTLY.
You need to have a 3-Phase-Inverter that will put out a "6-Hertz" starting speed and
hold that Frequency until the Engine starts.

Keep in mind that this will require a massive amount of Current,
enough to smoke the Generator's Windings in about 30-Seconds.

It would be a much better plan to simply see if your Engine has an optional 12V Starter.
If there is no optional Starter, get a bigger Generator that has one,
you'll spend less money in the long-run.

The single Phase thing won't even come close to working.
.
.
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money is not the problem, strength/injury is. can't handle bigger genset. can use dimmer to reduce initial power. yes, 50hz a rude shock from zero. motor is 66cc, running ulp. <150w pull to start it, so <sqrt3 phases will turn motor. commercial 500w dimmer with spring return to low should be easy. e-start kit will be sought, but little room for direct/planetary drive onto ratchet shaft, ring gear even less so. a pancake motor shape, [e-fan from car?] might go in. wattage/start torque unknown. last one was only 80w.