Doubly asymptotic trajectories of Lagrangian systems in homogeneous force fields
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.
scientific article; zbMATH DE number 1463346