Geodesic
Compatible Lie–Poisson brackets on the Lie algebras $e(3)$ and $so(4)$
Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 1, pp. 26-43 Cet article a éte moissonné depuis la source Math-Net.Ru

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We completely classify the compatible Lie–Poisson brackets on the dual spaces of the Lie algebras $e(3)$ and $so(4)$. The corresponding bi-Hamiltonian systems are the spinning tops corresponding to the classical cases of integrability of the Euler equations, the Kirchhoff equations, and the Poincaré–Zhukovskii equations.
Keywords: integrable system, bi-Hamiltonian manifold
Mots-clés : Lie–Poisson tensor. 
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A. V. Tsiganov. Compatible Lie–Poisson brackets on the Lie algebras $e(3)$ and $so(4)$. Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 1, pp. 26-43. http://geodesic.mathdoc.fr/item/TMF_2007_151_1_a1/

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