Nonrelativistic Geodesic Motion

We show that any second-order dynamic equationon a configuration space X R ofnonrelativistic time-dependent mechanics can be seen asa geodesic equation with respect to some (nonlinear)connection on the tangent bundle TX X of relativisticvelocities. We compare relativistic and nonrelativisticgeodesic equations, and study the Jacobi vector fieldsalong nonrelativistic geodesics.