The MacCullagh ellipsoid is defined by the equation:
:
where
is the energy and
are the components of the
angular momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
, given in body's principal reference frame, with corresponding
principal moments of inertia
The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceler ...
. The construction of such
ellipsoid was conceived by
James MacCullagh
James MacCullagh (1809 – 24 October 1847) was an Irish mathematician.
Early Life
MacCullagh was born in Landahaussy, near Plumbridge, County Tyrone, Ireland, but the family moved to Curly Hill, Strabane when James was about 10. He was the e ...
.
[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
* 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
{{Reflist
Rigid bodies