  Why would anyone wish to generalize the already unappetizing subject of rigid
body motion to an arbitrary number of dimensions? At first sight, the subject
seems to be both repellent and superfluous. The author will try to argue that
an approach involving no specifically three-dimensional constructs is actually
easier to grasp than the traditional one and might thus be generally useful to
understand rigid body motion both in three dimensions and in the general case.
Specific differences between the viewpoint suggested here and the usual one
include the following: here angular velocities are systematically treated as
antisymmetric matrices, a symmetric tensor $I$ quite different from the moment
of inertia tensor plays a central role, whereas the latter is shown to be a far
more complex object, namely a tensor of rank four. A straightforward way to
define it is given. The Euler equation is derived and the use of Noether's
theorem to obtain conserved quantities is illustrated. Finally the equation of
motion for two bodies linked by a spherical joint is derived to display the
simplicity and the power of the method.
