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Poisson Bracket and Lie-Poisson Schemes

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Symplectic Geometric Algorithms for Hamiltonian Systems

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Abstract

In this chapter, a clear Lie-Poisson Hamilton-Jacobi theory is presented. It is also shown how to construct a Lie-Poisson scheme integrator by generating function, which is different from the Ge-Marsden[GM88] method.

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Authors and Affiliations

  1. Institute of Computational Mathematics and Scientific/Engineering Computing, Beijing, 100190, China

    Kang Feng & Mengzhao Qin

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  1. Kang Feng
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  2. Mengzhao Qin
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© 2010 Zhejiang Publishing United Group, Zhejiang Science and Technology Publishing House, Hangzhou and Springer-Verlag Berlin Heidelberg

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Feng, K., Qin, M. (2010). Poisson Bracket and Lie-Poisson Schemes. In: Symplectic Geometric Algorithms for Hamiltonian Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01777-3_13

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