I'm looking for a way to calculate possible balanced positions of 5 equal masses on the circumference of a spinning wheel such that the distance along the circumference between the masses are all different, and no distance is an integer multiple of any of other the other distances. This is like the balanced centrifuge problem, but without defined slots.
Update... It may be taboo to cross-post to both Mathematics AND Engineering, but I did get step closer to the solution I'm seeking over there. https://engineering.stackexchange.com/a/54938/41450
I made the diagram below by taking an existing balanced arrangement and then moved the vectors nose to tail to create these pentagons. This particular balanced arrangement doesn't meet the criteria of distances on the circumference being non-integer multiples. I just need to figure out how to go the other way, and make distorted equal sided pentagons, and then see if the resulting arrangements are non-integer multiples.
