Mr Hayward, in his paper already referred to, has made great use of the mechanical conception of Angular Momentum.
Definition 1 The Angular Momentum of a particle about an axis is measured by the product of the mass of the particle, its velocity resolved in the normal plane, and the perpendicular from the axis on the direction of motion.
[*] The angular momentum of any system about an axis is the algebraical sum of the angular momenta of its parts.
As the rate of change of the linear momentum of a particle measures the moving force which acts on it, so the rate of change of angular momentum measures the moment of that force about an axis.
All actions between the parts of a system, being pairs of equal and opposite forces, produce equal and opposite changes in the angular momentum of those parts. Hence the whole angular momentum of the system is not affected by these actions and re-actions.
[*] When a system of invariable form revolves about an axis, the angular velocity of every part is the same, and the angular momentum about the axis is the product of the angular velocity and the moment of inertia about that axis.
[*] It is only in particular cases, however, that the whole angular momentum can be estimated in this way. In general, the axis of angular momentum differs from the axis of rotation, so that there will be a residual angular momentum about an axis perpendicular to that of rotation, unless that axis has one of three positions, called the principal axes of the body.
By referring everything to these three axes, the theory is greatly simplified. The moment of inertia about one of these axes is greater than that about any other axis through the same point, and that about one of the others is a minimum. These two are at right angles, and the third axis is perpendicular to their plane, and is called the mean axis.
[*] Let
