[HN Gopher] Jacobi Ellipsoid
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Jacobi Ellipsoid
Author : perihelions
Score : 18 points
Date : 2025-06-28 16:27 UTC (2 days ago)
(HTM) web link (en.wikipedia.org)
(TXT) w3m dump (en.wikipedia.org)
| masfuerte wrote:
| This is surprising, but less surprising when you realise it is
| rotating about one of the foci, not the centre.
| perihelions wrote:
| Hmm, 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.
| MycroftJones wrote:
| That page didn't have a formula, in either cartesian or polar
| coordinates, for the shape of the object. Lots of formulas, but I
| didn't see anything I could use to create a 3d mesh and print one
| of these things out on my printer.
| groos wrote:
| It's the general ellipsoid formula: x*2/a*2 + y*2/b*2 + z*2/c*2
| = 1, where a, b and c are all unequal. The interesting part is
| actually that this shape could be made of a liquid, held by
| gravitation and maintain this asymmetrical shape. Normally, one
| would imagine it would be ellipsoid of revolution, where two of
| the axes are equal.
|
| https://en.wikipedia.org/wiki/Ellipsoid
|
| To make a plot in software such as JMol, you really need
| parametric equations, which are also given in the above page.
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(page generated 2025-06-30 23:00 UTC)