保存先:
| 主要な著者: | , , |
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| フォーマット: | Preprint |
| 出版事項: |
2000
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| 主題: | |
| オンライン･アクセス: | https://arxiv.org/abs/math/0004018 |
| タグ: |
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目次:
- For a discrete mechanical system on a Lie group $G$ determined by a (reduced) Lagrangian $\ell$ we define a Poisson structure via the pull-back of the Lie-Poisson structure on the dual of the Lie algebra ${\mathfrak g}^*$ by the corresponding Legendre transform. The main result shown in this paper is that this structure coincides with the reduction under the symmetry group $G$ of the canonical discrete Lagrange 2-form $ω_\mathbb{L}$ on $G \times G$. Its symplectic leaves then become dynamically invariant manifolds for the reduced discrete system. Links between our approach and that of groupoids and algebroids as well as the reduced Hamilton-Jacobi equation are made. The rigid body is discussed as an example.