A few doubts regarding lagrnagian method to deal with motion of particles: 1) It seems like a heuristic method of solving for motion of a particle. In newtonian mechanics, you carefully consider all the forces and find out the particle's motion. In this, based on intuition you guess the paticle will move in such and such trajectory, decide the generalised coordinates and solve it. Am I right? 2) I was studying its proof when it said that ∂T / ∂x = 0. I don't understand this. T is kinetic energy which of course is in terms of velocity. Velocity is dx / dt. Then how come it is zero?