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where h is a constant vector. This result represents the conservation of angular momentum and contains three further constants of integration. Written out in component form as, of course, they had to be in the eighteenth century, these equations are termed the 'three integrals of areas' because they state that the sums of the products of the masses and the projections of the areas described by the line connecting the body m, to the origin onto the coordinate planes, are proportional to time. In vector form, we can see immediately that Eqn (9.15) defines a plane that remains fixed, however the masses move. If we take the centre of gravity as the origin, then any point in this plane has position vector r which satisfies r ■ h = 0, h being the sum of the angular momenta of all the particles in the system. It was Laplace who made this realization and, for the

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