Doubly Asymptotic Trajectories of Lagrangian Systems in Homogeneous Force Fields

被引：7

作者：

Bertotti, M. L. ^{[1
]}

Bolotin, S. V. ^{[2
]}

机构：

[1] Trento Univ, Dept Mech & Struct Engn, I-38050 Trento, Italy

[2] Moscow MV Lomonosov State Univ, Dept Math & Mech, Moscow 119899, Russia

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 1998年 / 174卷 / 01期

关键词：

58F05; 58E05; 34C37; 70H05; 34C35;

D O I：

10.1007/BF01759374

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study Lagrangian systems with symmetry under the action of a constant generalized force in the direction of the symmetry field. After Routh's reduction, such systems become nonautonomous with Lagrangian quadratic in time. We prove the existence of solutions tending to an orbit of the symmetry group as t ->+/- infinity. As an example, we study doubly asymptotic solutions for the Kirchhoff problem of a heavy rigid body in an infinite volume of incompressible ideal fluid performing a potential motion.

引用

页码：253 / 275

页数：23

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