Geodesic
Doubly asymptotic trajectories of Lagrangian systems and a problem by Kirchhoff
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 8 (1997) no. 2, pp. 93-100

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We consider Lagrangian systems with Lagrange functions which exhibit a quadratic time dependence. We prove the existence of infinitely many solutions tending, as \( t \rightarrow \pm \infty \), to an «equilibrium at infinity». This result is applied to the Kirchhoff problem of a heavy rigid body moving through a boundless incompressible ideal fluid, which is at rest at infinity and has zero vorticity. 
@article{RLIN_1997_9_8_2_a0,
     author = {Bertotti, Maria Letizia and Bolotin, Sergey V.},
     title = {Doubly asymptotic trajectories of {Lagrangian} systems and a problem by {Kirchhoff}},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {93--100},
     publisher = {mathdoc},
     volume = {Ser. 9, 8},
     number = {2},
     year = {1997},
     zbl = {0892.70012},
     mrnumber = {MR1485320},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1997_9_8_2_a0/}
}
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Bertotti, Maria Letizia; Bolotin, Sergey V. Doubly asymptotic trajectories of Lagrangian systems and a problem by Kirchhoff. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 8 (1997) no. 2, pp. 93-100. http://geodesic.mathdoc.fr/item/RLIN_1997_9_8_2_a0/