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.

On the Euler equation: bi-Hamiltonian structure and integrals in involution / C. Morosi, L. Pizzocchero. - In: LETTERS IN MATHEMATICAL PHYSICS. - ISSN 0377-9017. - 37:2(1996), pp. 117-135.

On the Euler equation: bi-Hamiltonian structure and integrals in involution

L. Pizzocchero
Ultimo
1996

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.
Euler equations on Lie algebras; Hamiltonian structures; Integrable systems
Settore MAT/07 - Fisica Matematica
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/191000
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