Momental Sentence Examples

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.

If p be the radius-vector 0J of the momental ellipsoid Ax+By+Czf=Me4 (I)

The motion of the body relative to 0 is therefore completely represented if we imagine the momental ellipsoid at 0 to roll without sliding on a plane fixed in space, with an angular velocity proportional at each instant to the radius-vector of the point of contact.

If A = B = C, the momental ellipsoid becomes a sphere; all axes through 0 are then principal axes, and the moment of inertia is the same for each.

This shows that the C.P. is the antipole of the line of intersection of its plane with the free surface with respect to the momental ellipse at the C.G.