Stability for Lagrangian relative equilibria of three-point-mass systems

Tanya Schmah; Cristina Stoica

doi:10.1088/0305-4470/39/46/012

Stability for Lagrangian relative equilibria of three-point-mass systems

Tanya Schmah^*, Cristina Stoica

^*Corresponding author for this work

Research output: Contribution to journal › Article

4 Citations (Scopus)

Abstract

In the present paper we apply geometric methods, and in particular the reduced energy-momentum (REM) method, to the analysis of stability of planar rotationally invariant relative equilibria of three-point-mass systems. We analyse two examples in detail: equilateral relative equilibria for the three-body problem, and isosceles triatomic molecules. We discuss some open problems to which the method is applicable, including roto-translational motion in the full three-body problem.

Original language	English
Article number	012
Pages (from-to)	14405-14425
Number of pages	21
Journal	Journal of Physics A: Mathematical and General
Volume	39
Issue number	46
DOIs	https://doi.org/10.1088/0305-4470/39/46/012
Publication status	Published - 17 Nov 2006

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AB - In the present paper we apply geometric methods, and in particular the reduced energy-momentum (REM) method, to the analysis of stability of planar rotationally invariant relative equilibria of three-point-mass systems. We analyse two examples in detail: equilateral relative equilibria for the three-body problem, and isosceles triatomic molecules. We discuss some open problems to which the method is applicable, including roto-translational motion in the full three-body problem.

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