III. Some new theorems on the motion of a body about a fixed point

Abstract

Poinsot constructs the motion of a rigid body about a fixed point under the action of no forces by means of an ellipsoid which has its centre at the fixed point and rolls on a fixed plane. In this manner the relations of the invariable line, and the instantaneous axis to each other and to the other parts of the body, may be found by solid geometry. It is evident that in many cases these relations are merely translations into the language of solid geometry of certain properties of the spherical ellipse.