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Published Online: 15 September 2005
Accepted: July 2005

Symplectic integrators: An introduction

American Journal of Physics 73, 938 (2005); https://doi.org/10.1119/1.2034523
Denis Donnellya)
  • Department of Physics, Siena College, Loudonville, New York 12211
    • Edwin Rogersb)
  • Department of Mathematics, Siena College, Loudonville, New York 12211
    • more...View Affiliations
    Abstract
    Symplectic integrators very nearly conserve the total energy and are particularly useful when treating long times. We demonstrate some of the properties of these integrators by exploring the structure of first-, second-, and fourth-order symplectic integrators and apply them to the simple harmonic oscillator. We consider numeric, geometric, and analytic aspects of the integrators with particular attention to the computed energies.

    ACKNOWLEDGMENTS

    The authors would like to acknowledge the help of anonymous reviewers, whose comments resulted in a greatly improved version of this paper.

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