Gravity graph

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A gravity graph is a kind of art "tool" that lets you draw nice geometric shapes. It has a board the size of a piece of paper that is weighted in the middle, each of the corners is connected to a piece of string and the strings are tied to a small rectangle (paralell to the board) about 1.5 feet from the board. Basiclly it is a board hanging by 4 strings. Then there is a pen that touches the middle of the paper (that is on the board) and it can bob up and down so that it touches the paper even if it's (=the board) moving up and down. Now to draw a shape you just swing the board and as it slows down and stops it draws nice geometrical shapes. For example, if you swing it in a circle you will get a spirle. Now I wanted to make something like that on the computer. First of all I have to simulate the swinging. I thought that I'd think of the strings as tense springs, and figure out the sum of the forces on each corner (spring+gravity), Then from those forces I'll check the sum of the forces at a right angle to each of the 3 axises of spin (x,y,z) and from that figure out the angular acceleration of each axis with Fx = Ia. Then I sum all of the forces around the center point to see how much it moves (translates) with F = ma. For every frame I'd callcuate the rotation by the angular acceleration and the position by the linear acceleration. Is this correct? The main problem that I see is that the same forces both spin and move, should the forces that I use to translate be weakened because of the force that is being used to spin? Or is there an easier way to do the whole thing? Thanks!

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It would appear to me at least that this problem would be equally represented by a flat plate connected to a pivot point by a semi-rigid rod which joined the plate at its centre of mass. This would simplify your calculations of the boards motion to resolving the bending and twisting in the end of the rod farthest from the pivot point.

Cheers,

Timkin

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Could you explain a little more please, I'm not sure what you mean.
Thanks.

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I think what he meant was, unless your string is ever allowed to go slack, you can model it as a stiff rod with a ball and socket join at each end, and get the same result. Springs are a pain, because although they are easy to set up initialy, they are a pain to make stable, especially when stiff.

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How would I model the "ball and socket" physicly (in a program)
Thanks.

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Why make it even that complicated?

You can probably get away with a 2d simulation of a particle orbiting the origin with a little drag.

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