Geodesic
A New Integrable Case for the Kirchhoff Equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 1, pp. 31-37

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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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     author = {V. V. Sokolov},
     title = {A {New} {Integrable} {Case} for the {Kirchhoff} {Equation}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {129},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_129_1_a3/}
}
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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/