My teacher asked us too prove that Hamiltons principle proves that newtons equations of motion hold for N particles. I'm not sure that i fully grasp the concept but this is my understanding so far: Using the lagrangian we can prove newtons law for specific situations, however Hamiltons principle allows us to make the specific situation into generalized coordintes. This is my understanding so far, but i feel that i don't completely understand. Why do we need it to be in generalized coordinates? Why does hamiltons principle allow it to change to generalized coordinates?