Lagrange’s Equations of Motion
Monday, November 18, 2013
  In this note we apply the Lagrange method of variation of constants to the basic Newton's equations by considering the force involved as a perturbation of the absence of forces. We get then a covariant expression of Newton equations on the space of inertial motions, and the force exerced to a simple body appears as the symplectic gradient of the perturbation potential, which gives by the way a covariant symplectic nature to the concept of force. Ref.