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The MacCullagh ellipsoid is defined by the equation:
where is the energy and are the components of the angular momentum, given in body's principal reference frame, with corresponding principal moments of inertia . The construction of such ellipsoid was conceived by James MacCullagh.
- ^ 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. [Transactions of the Royal Irish Academy, Vol. xxii. p. 139. Read April 23, 1849.]