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Multiplicity of Subharmonic solutions of Forces Hamiltonian systems near an equilibrium.

Maria Letizia Bertotti — 1989

Manuscripta mathematica

Doubly asymptotic trajectories of Lagrangian systems and a problem by Kirchhoff

Maria Letizia Bertotti; Sergey V. Bolotin — 1997

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We consider Lagrangian systems with Lagrange functions which exhibit a quadratic time dependence. We prove the existence of infinitely many solutions tending, as $t \to \pm \infty$ , 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.

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