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Using anti-gravity control is generally as simple as just willing yourself to fall in a certain direction.
It doesn't seem to be a physically strenuous activity, though it probably takes energy to move around. I'd say its about as exhausting as running except that you'll never get winded, just eventually feel tired.
You can't really train in anti-gravity movement to gain more speed because it is, more or less, a fixed ability. You can train in your control of it for the purpose of making flashy acrobatics and finicky moves using manipulated gravity to enhance certain maneuvers.
A good example of that is the fight the NH-17 nekovalkyrja Yuuko had in an arena. See here.
As for function, it... it's... well, part of the way the body works... so I guess it'd be physical.
How I've always used it is like this: Yamataians get drained by doing it, as it takes bodily energy to use the antigrav. NH-29, having more stamina, can do it much better and longer than a modern Yamataian can.
My rough estimate is, you can fly at top speed (20 mph?) for about 20 minutes before starting to feel hungry. Twenty minutes was the approximate unassisted battle time of the old NH-17 Nekovalkyrja, so that's where I get the number from.
No, you can't really train the capability for game balance reasons. If we start allowing one person to reach 80 mph or use it in more gravity, everyone will want custom tweaks on their ability and we won't hear the end of it. To be fair with everyone, this has to be fixed.
If your character has an overall better stamina, that's another thing. Your ability to do aerial, gravity-enhanced acrobatics is also separate from your intrinsic hovering ability.
The NH-29 is a lot faster and more nimble than Yamataians - I always intended the Yamataian to float, jump huge fences, and land softly, but never to zip around at cars speeds like a Nekovaklyrja. I've said this before.
Perhaps it would draw less confusion if instead of having the Yamataian CCG page lead to other species' pages, especially now-defunct ones, that Lord Wes were to write a page for the Yamataians based on how he wants them played?