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I present an intuitive answer to an often asked question: why is theintegrated difference K-U between the kinetic and potential energy the quantityto be minimized in Hamilton's principle?  Using elementary arguments, I map the problem of finding the path of a movingparticle connecting two points to that of finding the minimum potential energyof a static string. The mapping implies that the configuration of anon--stretchable string of variable tension corresponds to the spatial pathdictated by the Principle of Least Action; that of a stretchable string inspace-time is the one dictated by Hamilton's principle. This correspondenceprovides the answer to the question above: while a downward force curves thetrajectory of a particle in the (x,t) plane downward, an upward force of thesame magnitude stretches the string to the same configuration x(t).Comment: 7 pages, 4 figures. Submitted to the American Journal of Physic

Hamilton’s principle: Why is the integrated difference of the kinetic and potential energy minimized?