Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators

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

• Journal: Physics Letters A
• Year: 1988
• Volume: 133
• Issue: 3
• Pages: 134–139
• Publisher: Elsevier BV
• DOI: 10.1016/0375-9601(88)90773-6

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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