I've wondered this for ages, it's definitely been an area of reasearch over the last 100 years, but I've not heard much solid from it. It's certainly capable of providing for linear movement and or rotation, but I'm not sure if it operates on forces it generates or if it's "pushing" against gravity from the Earth, and have seen no "practical" propulsion system born from.

There's quite a few patents listed on rexresearch that have serious potential for use.

If it helps you decide if there's any weight to the claims, the patent was bought by what is now shell for £1000000 - which in the early 1900's was a significant sum.

Short of analyzing and recording changes in electromagnetic and gravitational fields based on cosmic bodies in relation to the gravitator, what would be the practical application of this?

It can provide for motive output...

I've not actually seen a practical propulsion system based on this principle, and it's been looked at intensely in some places. I've heard rumours of thirty feet per second from 50kV, and almost no current. As it's output seems dependant on distance/phase of moon it possibly suggests it's only useful whilst actually in a gravitational feild - but that said getting most of the way up would be a significant saving.

Nm/s per kW I think the EM-Drive/Q-thruster will prove to be a more efficient lifting system, personally. Especially as it doesn't stop working(assuming it does actually work) once you enter microgravity. Ofc to lift anything "worth lifting" would take megawatts, not kilowatts most likely - this isn't impossible to provide for, but difficult "cheap".