Uncle Owl Face would be proud of you
I'm not an engineer and high-school geometry was a very long time ago, but, yes, I believe the wash arm's patterns are nutations of an orbit. Euler's second law? Way too long ago.
Anyway, there were three wash arms from the post PotscrubberII era. This one, on the higher-end machines caused Consumer Reports to dethrone KA and announce (with tremendous reluctance, they were bought and sold to KA) that this dishwasher was better at cleaning. Much better.
A simple mechanism (looks like a cam to me, but I'm not an engineer) throws the arm out and then draws it back in during it's rotation. It isn't truly random, but it does make sure that even the further most corners of the top rack get thorough coverage.
A second variation also uses whirligigs on top of a regular arm (Frigidaire does that on some, still, today) and they were absolutely the most horrible, terrible, clog-prone, stupid, worthless trash GE ever put on the market, doing great harm to my opinion of them.
The third variation, the one still in use on the last of the Potscrubbers (the ones you get from Home Depot for 250-350$), doesn't nutate, it just rotates and sprays water through big holes. Does a pretty good job, given enough water, to be honest.
One must never upset the KA folks (we've had several ourselves and yes, they're wonderful, the very best, truly the holy grail, blah, blah, blah), but this design really would have made the 18" dishwashers clean well in the corners and it runs rings around everything else when you're dealing with truly dirty dishes.