Finsler geodesics of Lagrangian systems through Routh reduction
  We make use of a symmetry reduction technique called Routh reduction to show that the solutions of the Euler-Lagrange equations of a strongly convex autonomous Lagrangian which lie on a specific energy level can be thought of as geodesics of an associated Finsler function. 
T. Mestdag
math.DG math-ph math.MP