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arXiv · 1212.1955

Canonical equations of Hamilton with beautiful symmetry

Guo Liang·Qi Guo
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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 Schrödinger equation, a universal first-order differential system, can be expressed with the new canonical equations in a consistent way.

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Guo Liang, Qi Guo. 2012-12-10. Canonical equations of Hamilton with beautiful symmetry. https://arxiv.org/abs/1212.1955

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