We outline a story line that introduces Newtonian mechanics by employing conservation of energy to predict the motion of a particle in a one-dimensional potential. We show that incorporating constraints and constants of the motion into the energy expression allows us to analyze more complicated systems. A heuristic transition embeds kinetic and potential energy into the still more powerful principle of least action.
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LAGRANGIANS AND ACTION| April 01 2004
From conservation of energy to the principle of least action: A story line
Jozef Hanc, Edwin F. Taylor; From conservation of energy to the principle of least action: A story line. Am. J. Phys. 1 April 2004; 72 (4): 514–521. https://doi.org/10.1119/1.1645282
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