The symmetric representation of the rigid body equations and their discretization
The symmetric representation of the rigid body equations and their discretization
复制标题
刚体方程的对称表示及其离散化
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
T. Ratiu
中科院分区：
文献类型：
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作者：
A. Bloch;P. Crouch;J. Marsden;T. Ratiu
本文分析了广义刚体方程的连续和离散形式，以及这些方程在数值分析、最优控制和可积Hamilton系统中的作用。特别地，我们给出了刚体方程在笛卡尔积SO（n）× SO（n）上的对称表示，并研究了其相应的辛结构.我们描述了这些想法与离散可积系统的Moser-Veselov理论和变分辛积分理论的关系。
在Bloch等人（Bloch AM，Crouch P，Marsden J E和Ratiu T S 1998 Proc. IEEE Conf. on Decision and Control 37 2249-54）中可以找到关于本文中讨论的思想的初步工作。
This paper analyses continuous and discrete versions of the generalized rigid body equations and the role of these equations in numerical analysis, optimal control and integrable Hamiltonian systems. In particular, we present a symmetric representation of the rigid body equations on the Cartesian product SO(n) × SO(n) and study its associated symplectic structure. We describe the relationship of these ideas with the Moser–Veselov theory of discrete integrable systems and with the theory of variational symplectic integrators.
Preliminary work on the ideas discussed in this paper may be found in Bloch et al (Bloch AM, Crouch P, Marsden J E and Ratiu T S 1998 Proc. IEEE Conf. on Decision and Control 37 2249–54).