I am trying to find the best way to determine whether a spherical shell would stabilize in a certain orientation when falling. Assumptions I need to take into account: The sphere is spinning with some random angualr velocity for each axis The density of the shell is higher at the +x extreme and decreases until the density becomes uniform for the -x half of the shell. This density gradient can vary. It seems like it should be simple, but I must be missing something. That's what happens when a mathematician pretends to be an engineer.