2010/02/23

The principle of Hamiltonianization of physics

The theoretical development of the laws of motion of bodies is of such interest and importance, that it has engaged the attention of all the most eminent mathematicians, since the invention of dynamics as a mathematical science by Galileo...
Among the sucessors of those illustrious men, Lagrange has perhaps done more than any other analyst, to give extent and harmony to such deductive researches, by showing that the most varied consequences respecting the motions of systems of bodies may be derived from one radical formula[Lagrange's equations]; the beauty of the method so suiting the dignity of the results, as to make his great work a kind of scientific poem.

W. R. Hamilton, 1834