There is a way of _arriving_ at that subtraction, rather than just throwing it out there. A resource I created: Calculus of Variations as applied in physics:

There is a way of _arriving_ at that subtraction, rather than just throwing it out there. A resource I created: Calculus of Variations as applied in physics: http://cleonis.nl/physics/phys256/calculus_variations.php http://cleonis.nl/physics/phys256/calculus_variations.php Hamilton's stationary action: http://cleonis.nl/physics/phys256/energy_position_equation.php http://cleonis.nl/physics/phys256/energy_position_equation.p... In that resource I show why it works. In an earlier answer I gave more information about that resource. To find that earlier answer: go up to the entire thread, and search on the page for my nick: Cleonis