Doubly asymptotic trajectories of Lagrangian systems in homogeneous force fields
type: Item
instance of: scholarly article
title: Doubly asymptotic trajectories of Lagrangian systems in homogeneous force fields
zbMATH Open document ID: 0971.70021
DOI: 10.1007/BF01759374
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2001-11-01T00:00:00Z
review text: This paper studies Lagrangian systems with symmetry under the action of a constant generalized force in the direction of symmetry field. Due to this fact and since the kinetic energy does not depend on this direction, the corresponding coordinate can be ignored. Then the Routh's reduction allows to represent such systems as nonautonomous systems with Lagrangian quadratic in time. The authors prove the existence of solutions which approach an orbit of the symmetry group as \(t\to\pm\infty\). As an application, the authors study doubly asymptotic solutions of Kirchhoff problem for a heavy rigid body in an infinite volume of incompressible ideal fluid performing a potential motion.
Mathematics Subject Classification ID: 70H33
Mathematics Subject Classification ID: 70H03
Mathematics Subject Classification ID: 37N05
Mathematics Subject Classification ID: 70E99
zbMATH DE Number: 1463346
zbMATH Keywords: quadratic in time Lagrangian
zbMATH Keywords: Lagrangian systems with symmetry
zbMATH Keywords: generalized force
zbMATH Keywords: kinetic energy
zbMATH Keywords: Routh's reduction
zbMATH Keywords: existence of solutions
zbMATH Keywords: doubly asymptotic solutions
zbMATH Keywords: Kirchhoff problem
author: Maria Letizia Bertotti
author: S. V. Bolotin
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1463346