Jacobi ellipsoid

oblate ellipsoid under equilibrium

Wikidata entity: Q33728375

P2534	defining formula	Math	$\begin{aligned} Δ (u; a, b, c) & = \sqrt{(a^{2} + u) (b^{2} + u) (c^{2} + u)} \\ a^{2} b^{2} \int_{0}^{\infty} \frac{d u}{(a^{2} + u) (b^{2} + u) Δ (u; a, b, c)} & = c^{2} \int_{0}^{\infty} \frac{d u}{(c^{2} + u) Δ (u; a, b, c)} \\ \frac{Ω^{2}}{G M} & = \frac{3}{2} \int_{0}^{\infty} \frac{u d u}{(a^{2} + u) (b^{2} + u) Δ (u; a, b, c)} \end{aligned}$	???
P7235	in defining formula	Math	$a$	???
P7235	in defining formula	Math	$b$	???
P7235	in defining formula	Math	$G$	???
P7235	in defining formula	Math	$M$	???
P7235	in defining formula	Math	$c$	???
P7235	in defining formula	Math	$Ω$	???
P7235	in defining formula	Math	$\frac{3}{2}$	???
P31	instance of	...	Q24034552 (mathematical concept)	mathematical concept
P138	named after	...	Q76564 (Carl Gustav Jacob Jacobi)	Carl Gustav Jacob Jacobi
P5555	schematic	CommonsMedia	http://commons.wikimedia.org/wiki/Special:FilePath/Jacobi-ellipsoid-dimensions-2.svg	???
P279	subclass of	...	Q61567790 (tri-axial ellipsoid)	tri-axial ellipsoid

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