Since they are essentially positive the quadric is an ellipsoid; it is called the momental ellipsoid at 0.
A limitation is thus imposed on the possible forms of the momental ellipsoid; e.g.
If all the masses lie in a plane (1=0) we have, in the notation of (25), c2 = o, and therefore A = Mb, B = Ma, C = M (a +b), so that the equation of the momental ellipsoid takes the form b2x2+a y2+(a2+b2) z1=s4.
It possesses thi property that the radius of gyration about any diameter is half thi distance between the two tangents which are parallel to that diameter, In the case of a uniform triangular plate it may be shown that thi momental ellipse at G is concentric, similar and similarly situatec to the ellipse which touches the sides of the triangle at their middle points.
The relation between these axes may be expressed by means of the momental ellipsoid at 0.
