  The dynamics defined by a force field which is positively homogeneous of
degree $-3$ can always be reduced, by simply constraining it. The dimension of
the phase space is reduced by two dimensions, while it may only be reduced by
one dimension if the degree of homogeneity is different from $-3$. This remark
is an elegant foundation of Appell's projective dynamics. We show how it
relates to Kn\"orrer's remark on the correspondence between the Neumann
potential on a sphere and the geodesic motion on an ellipsoid.
