On the euler equation: Bi-Hamiltonian structure and integrals in involution |
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Authors: | Carlo Morosi Livio Pizzocchero |
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Institution: | (1) Dipartimento di Matematica, Politecnico di Milano, Piazza L. da Vinci 32, I-20133 Milan, Italy;(2) Dipartimento di Matematica, Università di Milano, Via C. Saldini 50, I-20133 Milan, Italy;(3) Sezione di Milano, Istituto Nazionale di Fisica Nucleare, Italy |
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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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Keywords: | 58F05 58F07 70Exx 70Hxx |
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