Center of gravity optimization

What would be the most efficient way to take in several weights, then have MATLAB optimize the position of each weight to meet a correct center of gravity?

[Fangjun Jiang]

Your question is vague. If I tell you that I have 4 weights, 4lbs, 3lbs, 2lbs and 1lbs, can you tell me where is the CG?

[Will]

Sorry I suppose that was too vague.

Lets say there is a plank of wood with negligible weight that has length x. I want the center of gravity to be located at x/2. The program would then optimize the locations of each weight to give the center of gravity as x/2.

[Will]

Also with my application, the weight could not be stacked.

Answer 1

[Walter Roberson]

Is it required to use all weights? If not then put the lighter weight at the end of the plank, and put the heavier weight proportionally in at distance L2 = w1/w2 * x/2 from the center

[Will]

It will be required to use all of the weights. I was just using the plank of wood as an example.

The real application is for determining the placement of boards into a stack of a CubeSat pico-satellite. The center of gravity of the satellite has to be within 2 cm of its geometric center. The boards already have their mass centered, so the only parameter to look at is the position of the boards in the stack.

I can do most of the basics of MATLAB, but had no clue where to start for doing an optimization like this.