(Yes, I have searched the other posts and each one comes up deficient for what I want.) Why must the Lagrangian be extremized? And why it is of the form L = T – V? BUT I HAVE CAVEATS! Please do it from first principles WITHOUT an understanding of F=ma. (And, yes, I understand the calculus of variations.) In other words, I have read, many times, that that form of the Lagrangian is SELECTED to ensure Newton’s law. I don’t like that “SELECTED” nonsense. I am looking for an intuitive understanding of why THAT form must be extremized. The first answer here comes close: http://www.quora.com/Laymans-Terms/What-is-a-Lagrangian [Broken] But I do not like that answer because.... I do not want to hear any anthropomorphic explanation, e.g.: “The ball wants to…” or “The object desires…” For then I would just ask you “WHY does the ball want to…” So first please explain it with regard to K.E. and Potential E. just so I can understand that much... And then, to make matters worse, I am hoping you can repeat the answer WITHOUT using the words KINETIC or POTENTIAL. (Because if you use those words, you are imbuing your response with a tacit awareness of F=ma) So, instead, please use 0.5mv-squared and mgh (yes, you can focus on particle that has been thrown into the air: I am fine with that) In other words,for a ball thrown into the air and without any reference to Lagrangian, Kinetic or Potential or Action Why is the following extremized: the mass weighted square of the velocity halved the negative of the mass weighted height If the constraints I placed on the possible answer are excessive, please tell me why. For it might be that such observational constraints are a necessary bridge between the intuition and the mathematical formalism. It may simply be that "the ball really DOES want to."