Geodesic
Spatially distributed classical Lagrangian mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 101 (1994) no. 3, pp. 369-373

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It is well known that the existence of two nontrivial integrals of the motion makes it possible to parametrize the motion of a Lagrangian rigid body by two variables. On the basis of this fact it is shown that certain combinations of the quantities that characterize the trajectory of such a body satisfy well-known nonlinear equations: sine–Gordon, Korteweg–de Vries, Klein–Gordon, and nonlinear Schrödinger equation. 
@article{TMF_1994_101_3_a4,
     author = {E. I. Bogdanov},
     title = {Spatially distributed classical {Lagrangian} mechanics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {369--373},
     publisher = {mathdoc},
     volume = {101},
     number = {3},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_101_3_a4/}
}
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E. I. Bogdanov. Spatially distributed classical Lagrangian mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 101 (1994) no. 3, pp. 369-373. http://geodesic.mathdoc.fr/item/TMF_1994_101_3_a4/