Relativistic and Non-relativistic Equations of Motion
  It is shown that any second order dynamic equation on a configuration space $X$ of non-relativistic time-dependent mechanics can be seen as a geodesic equation with respect to some (non-linear) connection on the tangent bundle $TX\to X$ of relativistic velocities. Using this fact, the relationship between relativistic and non-relativistic equations of motion is studied. 
L.Mangiarotti and G.Sardanashvily