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The Lagrangian and Hamilton's Principle of Least Action*
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Richard Feynman is widely acknowledged as one of the finest 20th century physicist that has lived and his doctoral thesis was titled "The Principle of Least Action in Quantum Mechanics". Newton' laws of motion can be derived from this principle and is applicable in many branches of science. First expressed by the mathematician Maupertuis (1698 - 1759)- "Nature is thrifty in all its ways", variants of the principle are found in the works of other famous mathematicians (Gauss and Fermat). Fermat expressed "The path taken between two points by a ray of light is the path that can be traversed in the least time" and from this some laws of reflection and refraction can be determined.Other matematicians such as Euler and Lagrange (co founder of variational calculus) began to give the principle a more formal mathematical basis and this was developed later by Hamilton. The principle of least action has, to me, similarity to the observation that systems in equilibrium migrate to a state of minimal energy and moreoften this energy state is one where the energy may not be used again analogous to the concept of entropy where energy is continously degraded in processes to a state where is no longer useful. The point that fascinates me is that nature acts without knowledge of the laws of science or mathematics that humans have formulated and as such may simply be obeying a few natural principles of which the manifestations are myriad and complex.