Canonical equations of Hamilton with beautiful symmetry
Abstract
The Hamiltonian formulation plays the essential role in constructing the framework of modern physics. In this paper, a new form of canonical equations of Hamilton with the complete symmetry is obtained, which are valid not only for the first-order differential system, but also for the second-order differential system. The conventional form of the canonical equations without the symmetry [Goldstein et al., Classical Mechanics, 3rd ed, Addison-Wesley, 2001] are only for the second-order differential system. It is pointed out for the first time that the number of the canonical equations for the first-order differential system is half of that for the second-order differential system. The nonlinear Schr\"{o}dinger equation, a universal first-order differential system, can be expressed with the new canonical equations in a consistent way.
Keywords
Cite
@article{arxiv.1212.1955,
title = {Canonical equations of Hamilton with beautiful symmetry},
author = {Guo Liang and Qi Guo},
journal= {arXiv preprint arXiv:1212.1955},
year = {2012}
}
Comments
11 pages, no figures