alt Hacker NewsHmm, that can't be true; it's of uniform density, and the thing it's rotating about has to be its center of mass.
What's odd about it (to me) is the optimal solution isn't symmetric (cylindrically symmetric). It's an intuition trap that you'd expect symmetric solutions. If the Wikipedia history is to be believed, Lagrange fell for this wrong assumption, and there was a 45-year gap before anyone noticed the subtle wrongness of it.
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namibj • today at 1:31 AM
Remember the spontaneously flipping spinning hammer on the ISS?
...rotation for sufficiently non-spherical(-cow) objects in free fall is kinda weird.
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It has a lower symmetry than cylindrical, but it still has axes of symmetry and planes of symmetry and a center of symmetry.
The equilibrium condition only forces the symmetry condition that the points of intersection between any straight line that passes through the center of rotation with the surface of the body must be equidistant to the center of rotation.
This symmetry condition is satisfied by the symmetry group of the rectangular parallelepiped, which is also the symmetry group of the triaxial ellipsoid.