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arXiv · 1811.03184

The Symmetric Representation of the Generalized Rigid Body Equations and Symplectic Reduction

Tomoki Ohsawa
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Abstract

We show that a symplectic reduction of the symmetric representation of the generalized $n$-dimensional rigid body equations yields the $n$-dimensional Euler equation. This result provides an alternative to the more elaborate relationship between these equations established by Bloch, Crouch, Marsden, and Ratiu. Specifically, we exploit the inherent $\mathsf{Sp}(2n,\mathbb{R})$-symmetry in the symmetric representation to present its relationship with the Euler equation via symplectic reduction facilitated by the dual pair recently developed by Skerritt and Vizman.

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Tomoki Ohsawa. 2018-11-07. The Symmetric Representation of the Generalized Rigid Body Equations and Symplectic Reduction. https://doi.org/10.1088/1751-8121%2Fab20db

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