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arXiv · 1401.1096

A Differential Integrability Condition for Two-Dimensional Hamiltonian Systems

Ali Mostafazadeh
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Abstract

We review, restate, and prove a result due to Kaushal and Korsch [Phys. Lett. A 276, 47 (2000)] on the complete integrability of two-dimensional Hamiltonian systems whose Hamiltonian satisfies a set of four linear second order partial differential equations. In particular, we show that a two-dimensional Hamiltonian system is completely integrable, if the Hamiltonian has the form $H=T+V$ where $V$ and $T$ are respectively harmonic functions of the generalized coordinates and the associated momenta.

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Ali Mostafazadeh. 2014-01-06. A Differential Integrability Condition for Two-Dimensional Hamiltonian Systems. https://doi.org/10.14311/ap.2014.54.0139

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