Authors

Ge Zhong, Jerrold E. Marsden

Abstract

We present results on numerical integrators that exactly preserve momentum maps and Poisson brackets, thereby inducing integrators that preserve the natural Lie-Poisson structure on the duals of Lie algebras. The techniques are baseda on time-stepping with the generating function obtained as an approximate solution to the Hamilton-Jacobi equation, following ideas of deVogelaére, Channel,, and Feng. To accomplish this, the Hamilton-Jacobi theory is reduced from T∗G to g∗, where g is the Lie algebra of a Lie group G. The algorithms exactly preserve any additional conserved quantities in the problem. An explicit algorithm is given for any semi-simple group and in particular for the Euler equation of rigid body dynamics.

Citation

BibTeX

@article{Zhong_1988,
  title={{Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators}},
  volume={133},
  ISSN={0375-9601},
  DOI={10.1016/0375-9601(88)90773-6},
  number={3},
  journal={Physics Letters A},
  publisher={Elsevier BV},
  author={Zhong, Ge and Marsden, Jerrold E.},
  year={1988},
  pages={134--139}
}

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References

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