Attraction force of a disk

[lancelot]

I only just now realized that mathematically the inverse-square force field of a disk is not the same as the field generated by a point mass/charge. In Algodoo they are the same because Algodoo calculates the attraction force only with respect to the center of mass. In fact, the trajectory of a particle in the field of an attracting disk is not a conic (at least not in the general case).

It would be nice to be able to model the attraction force of a 2D shape. Having a way to model point masses is definitely useful too, but maybe there can be an option to tesselate shapes that have the attraction property (and then possibly to use known closed forms for simple shapes).

[Someone Else]

I agree that the way Algodoo simulates attraction isn't always accurate- probably best demonstrated by this scene by Davids40:

gauss gun

davidz

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It works because the of mass of a C-shaped polygon is in open space, and it is possible to position another grom such that its center of mass is very close to the center of mass of the C-shape, so the force between them is immense, even if the attraction parameter isn't that large.

How this could be improved, well, I don't know. Breaking geoms into a multitude of small attraction pieces would cause a lot of lag...
Does anyone know of any sort of fancy math that would calculate this directly, at least for a circle or box?