  Aghannan and Rouchon proposed a new design method of asymptotic observers for
a class of nonlinear mechanical systems: Lagrangian systems with configuration
(position) measurements. The observer is based on the Riemannian structure of
the configuration manifold endowed with the kinetic energy metric and is
intrinsic. They proved local convergence. When the system is conservative, we
propose a globally convergent intrinsic reduced-observer based on the Jacobi
metric. For non-conservative systems the observer can be used as a complement
to the one of Aghannan and Rouchon. More generally the reduced-observer
provides velocity estimation for geodesic flow with position measurements. Thus
it can be (formally) used as a fluid flow soft sensor in the case of a perfect
incompressible fluid. When the curvature is negative in all planes the geodesic
flow is sensitive to initial conditions. Surprisingly this instability yields
faster convergence.
