Geodesic
A New Integrable Case for the Kirchhoff Equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 1, pp. 31-37 Cet article a éte moissonné depuis la source Math-Net.Ru

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A new integrable case is found for the Kirchhoff equation. The additional integral of motion is a fourth-degree polynomial, the principal metric is diagonal with the eigenvalues $a_1=a_2=1$ and $a_3=2$, and the other two metrics are nondiagonal. 
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V. V. Sokolov. A New Integrable Case for the Kirchhoff Equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 1, pp. 31-37. http://geodesic.mathdoc.fr/item/TMF_2001_129_1_a3/

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