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The MacCullagh ellipsoid is defined by the equation:

${\displaystyle {\frac {x^{2}}{A}}+{\frac {y^{2}}{B}}+{\frac {z^{2}}{C}}=2E,}$

where ${\displaystyle E}$ is the energy and ${\displaystyle x,y,z}$ are the components of the angular momentum, given in body's principal reference frame, with corresponding principal moments of inertia ${\displaystyle A,B,C}$. The construction of such ellipsoid was conceived by James MacCullagh.

See also

• Dzhanibekov effect
• Poinsot's ellipsoid

References

1. On the Rotation of a Solid Body round a Fixed Point; being an account of the late Professor Mac Cullagh's Lectures on that subject. Compiled by the Rev. Samuel Haughton, Fellow of Trinity College, Dublin.

• Rigid bodies