Thanks for the rating!, the mouse controls are a result of the fact that websites aren't allowed to mess with your cursor position, the downloadable version has normal controls.
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Just got done playing around with it. Looks like you're "stationary" (i.e. not rotating) when your cursor is at a central location. Any deviation from that central location sets you rotating, endlessly, in the direction of deviation (with greater magnitudes causing faster rotation). It is a very challenging control system, but there IS a logic to it!