Long time exposures with a small iris opening on a camera can capture movement beautifully and it's possible to experiment so that you get just the right amount of sharpness (on still and slow moving parts of the picture) mixed with speedy blur. Black and white photographs really are the forté for this but you can do it in colour too... hmm must try some colourful fairground scenes :)
Painting the idea of movement was done really well by Monet in his picture of a lady battling with a blowy brolly, capturing the motion of the wind by it's effect on an object, be it skirts of fabric or the umbrella itself.
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One thing I've never managed to capture is the way a field of long grass ripples in waves when the wind is blowing across it. Photographs don't seem to get it right so maybe painting the idea of it might work... perhaps in a vanGogh style.
Anyway these are my two different styles of dancing pic. I think any painting I take from these will be just totally swirling and blurry just to take it that one step further :)
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Would love to see what you can come up with to represent the movement of dancing...