We consider Lagrangian systems with Lagrange functions which exhibit a quadratic time dependence. We prove the existence of infinitely many solutions tending, as , 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.
Consideriamo sistemi lagrangiani con funzione lagrangiana dipendente in modo quadratico dal tempo. Proviamo l'esistenza di infinite soluzioni che tendono, quando ad un «equilibrio all'infinito». Il risultato è applicato al problema di Kirchhoff di un corpo rigido mobile in un fluido ideale incomprimibile illimitato, che è in quiete all'infinito ed ha vorticità nulla.
@article{RLIN_1997_9_8_2_93_0,
author = {Maria Letizia Bertotti and Sergey V. Bolotin},
title = {Doubly asymptotic trajectories of Lagrangian systems and a problem by Kirchhoff},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
volume = {8},
year = {1997},
pages = {93-100},
zbl = {0892.70012},
mrnumber = {1485320},
language = {en},
url = {http://dml.mathdoc.fr/item/RLIN_1997_9_8_2_93_0}
}
Bertotti, Maria Letizia; Bolotin, Sergey V. Doubly asymptotic trajectories of Lagrangian systems and a problem by Kirchhoff. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 8 (1997) pp. 93-100. http://gdmltest.u-ga.fr/item/RLIN_1997_9_8_2_93_0/
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