Stability of Hamiltonian systems with three degrees of freedom and the three body-problem
type: Item
instance of: scholarly article
title: Stability of Hamiltonian systems with three degrees of freedom and the three body-problem
zbMATH Open document ID: 1175.70019
author: José Edmundo Mansilla
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 2009-06-02T00:00:00Z
review text: Results are obtained about formal stability and instability of Hamiltonian systems with three degrees of freedom, two equal frequencies and the matrix of the linear part is not diagonalizable, in terms of the coefficients of the development in Taylor series of the Hamiltonian of the system. The results are applied to the study of stability of the Lagrangian solutions of the Three Body-Problem in the case in which the center of mass is over the curve \(\rho_*\), on the border of the region of linear stability of Routh. The curve \(\rho_*\) is divided symmetrically in three arcs in such a way that if the center of mass of the three particles lies on the central arc, the Lagrangian solution is unstable in the sense of Liapunov (in finite order), while if the center of mass determines one point that lies on one of the other two arcs of \(\rho_*\), then the Lagrangian solution is formally stable.
Mathematics Subject Classification ID: 70H14
Mathematics Subject Classification ID: 70F07
zbMATH DE Number: 5560717
zbMATH Keywords: 3-Body Problem
zbMATH Keywords: Lagrange solutions
zbMATH Keywords: normal form
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: s10569-005-5360-6
OpenAlex ID: W1985224563
cites work: Q5838047
cites work: Q5559761
cites work: Q5329596
DOI: 10.1007/S10569-005-5360-6
description: scientific article; zbMATH DE number 5560717