Replying to:
-=Dark_Angel=-, P.I. 14-Apr-04/11:25 AM
Lying prone doesn't add additional problems. Doing it upsidedown standing on your neck is pointless. How do you know how far over to tilt your torso and legs? You want its centre of mass to be in the same place as the centre of mass of your head (which is why you can simply use your 1/2 * TOTAL_SYSTEM equation), so you need to know the centre of mass of the HEAD, and of the TORSOARMSLEGS. But given these you can obtain the result just as easily lying prone. Observe,

Let X be the centre of mass of the HEAD
Let Y be the centre of mass of the TORSOARMSLEGS
Let Z be the weight of the body

Lying prone, with the pivot at the neck and weight ADDEDWEIGHT positioned on the head's centre of mass (ie on its face) to balance the system, we can find HEAD as follows:

Consider these two equations (the first is obtained by equating moments, the second is just the fact that HEAD + TORSOARMSLEGS is the weight of the whole body)

(1) (HEAD + ADDEDWEIGHT) * X = TORSOARMSLEGS * Y
(2) HEAD + TORSOARMSLEGS = Z

There are two unknowns - HEAD and TORSOARMSLEGS - and two equations. So we can solve (1) and (2) to obtain HEAD as required.

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