  We consider a natural mechanical system on a Finsler manifold and study its
\emph{curvature} using the intrinsic Jacobi equations (called \emph{Jacobi
curves}) along the extremals of the least action of the system. The curvature
for such a system is expressed in terms of the Riemann curvature and the Chern
curvature (involving the gradient of the potential) of the Finsler manifold and
the Hessian of the potential w.r.t. a Riemannian metric induced from the
Finslerian metric. As an application, we give sufficient conditions for the
Hamiltonian flows of the least action to be hyperbolic and show new examples of
Anosov flows.
