# Gravity graph

1. Feb 10, 2006

### daniel_i_l

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!