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Symplectic Integration of Hamiltonian Systems using Polynomial Maps

Govindan Rangarajan
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Abstract

In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast and accurate. In this paper, we propose such a symplectic integration algorithm using polynomial map refactorization of the symplectic map representing the Hamiltonian system. This method should be particularly useful in long-term stability studies of particle storage rings in accelerators.

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Govindan Rangarajan. 2001-06-21. Symplectic Integration of Hamiltonian Systems using Polynomial Maps. https://doi.org/10.1016/s0375-9601(01)00409-1

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