| Abstrakt: |
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 (Bloch et al 2002 Nonlinearity15 1309–41). Specifically, we exploit the inherent -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 (Skerritt and Vizman 2019 J. Geom. Mech. 11 255–75). [ABSTRACT FROM AUTHOR] |
