The MacCullagh ellipsoid is defined by the equation:
:
where
is the energy and
are the components of the
angular momentum
Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of Momentum, linear momentum. It is an important physical quantity because it is a Conservation law, conserved quantity – the total ang ...
, given in body's principal reference frame, with corresponding
principal moments of inertia . The construction of such
ellipsoid
An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional Scaling (geometry), scalings, or more generally, of an affine transformation.
An ellipsoid is a quadric surface; that is, a Surface (mathemat ...
was conceived by
James MacCullagh
James MacCullagh (1809 – 24 October 1847) was an Irish mathematician and scientist. He served as the Erasmus Smith's Professor of Mathematics at Trinity College Dublin beginning in 1835, and in 1843, he was appointed as the Erasmus Smith' ...
.
[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. ransactions of the Royal Irish Academy, Vol. xxii. p. 139. Read April 23, 1849./ref>
]
See also
* Dzhanibekov effect
The tennis racket theorem or intermediate axis theorem, is a kinetic phenomenon of classical mechanics which describes the movement of a rigid body with three distinct principal moments of inertia. It has also been dubbed the Dzhanibekov eff ...
* Poinsot's ellipsoid
In classical mechanics, Poinsot's construction (after Louis Poinsot) is a geometrical method for visualizing the torque-free motion of a rotating rigid body, that is, the motion of a rigid body on which no external forces are acting. This motion ha ...
References
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Rigid bodies