Abstract
We propose a bi-Hamiltonian formulation of the Euler equation for the free n-dimensional rigid body moving about a fixed point. This formulation lives on the ‘physical’ phase space so(n), and is different from the bi-Hamiltonian formulation on the extended phase space sl(n), considered previously in the literature. Using the bi-Hamiltonian structure on so(n), we construct new recursion schemes for the Mishchenko and Manakov integrals of motion.
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Morosi, C., Pizzocchero, L. On the euler equation: Bi-Hamiltonian structure and integrals in involution. Letters in Mathematical Physics 37, 117–135 (1996). https://doi.org/10.1007/BF00416015
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DOI: https://doi.org/10.1007/BF00416015