Chasle's theorem states that any general displacement of a rigid body can be represented by a translation plus a rotation. The theorem suggests that it ought to be possible to split the problem of a rigid body motion into two separate phases, one concerned solely with the translation motion of the body, the other, with its rotational motion. Of course, if one point of the body is fixed the separation is obvious, for then there is only a rotational motion about the fixed point, without any translation. But even for a general type of motion such a separation is often possible. The six coordinates needed to describe the motion have already been formed into two sets in accordance with such a division: the three coordinates, of a point fixed in the rigid body to describe the translation motion and say, the three Euler angles for the motion about the point. If, further, the origin of the body system is chosen to be the centre of mass, the total angular momentum divides naturally into contributions from the translation of the centre of mass and from the rotation about the centre of mass. The former term will involve only the Cartesian coordinates of the centre of mass, the latter only the angle coordinates.

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