Does anyone know a text which justifies why the Lagrangian approach works? This text and many others I have encountered just start with the Principle of Least Action taken as given and go from there but I'm left wondering why we define the Action as this object and why we should expect it to be minimised for the physical trajectory in the first place.
Failing a full derivation from the ground up, a proof of the equivalence to Newtonian mechanics would be interesting.
Failing a full derivation from the ground up, a proof of the equivalence to Newtonian mechanics would be interesting.