  By identifying Hamiltonian flows with geodesic flows of suitably chosen
Riemannian manifolds, it is possible to explain the origin of chaos in
classical Newtonian dynamics and to quantify its strength. There are several
possibilities to geometrize Newtonian dynamics under the action of conservative
potentials and the hitherto investigated ones provide consistent results.
However, it has been recently argued that endowing configuration space with the
Jacobi metric is inappropriate to consistently describe the
stability/instability properties of Newtonian dynamics because of the
non-affine parametrization of the arc length with physical time. To the
contrary, in the present paper, it is shown that there is no such inconsistency
and that the observed instabilities in the case of integrable systems using the
Jacobi metric are artefacts.
