dorsal/arxiv
View SchemaHamilton's principle: why is the integrated difference of kinetic and potential energy minimized?
| Authors | Alberto G. Rojo |
|---|---|
| Categories | |
| ArXiv ID | physics/0504016 |
| URL | https://arxiv.org/abs/physics/0504016 |
| DOI | 10.1119/1.1930887 |
Abstract
I present an intuitive answer to an often asked question: why is the integrated difference K-U between the kinetic and potential energy the quantity to be minimized in Hamilton's principle? Using elementary arguments, I map the problem of finding the path of a moving particle connecting two points to that of finding the minimum potential energy of a static string. The mapping implies that the configuration of a non--stretchable string of variable tension corresponds to the spatial path dictated by the Principle of Least Action; that of a stretchable string in space-time is the one dictated by Hamilton's principle. This correspondence provides the answer to the question above: while a downward force curves the trajectory of a particle in the (x,t) plane downward, an upward force of the same magnitude stretches the string to the same configuration x(t).
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"abstract": "I present an intuitive answer to an often asked question: why is the\nintegrated difference K-U between the kinetic and potential energy the quantity\nto be minimized in Hamilton\u0027s principle?\n Using elementary arguments, I map the problem of finding the path of a moving\nparticle connecting two points to that of finding the minimum potential energy\nof a static string. The mapping implies that the configuration of a\nnon--stretchable string of variable tension corresponds to the spatial path\ndictated by the Principle of Least Action; that of a stretchable string in\nspace-time is the one dictated by Hamilton\u0027s principle. This correspondence\nprovides the answer to the question above: while a downward force curves the\ntrajectory of a particle in the (x,t) plane downward, an upward force of the\nsame magnitude stretches the string to the same configuration x(t).",
"arxiv_id": "physics/0504016",
"authors": [
"Alberto G. Rojo"
],
"categories": [
"physics.ed-ph",
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],
"doi": "10.1119/1.1930887",
"title": "Hamilton\u0027s principle: why is the integrated difference of kinetic and potential energy minimized?",
"url": "https://arxiv.org/abs/physics/0504016"
},
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