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Geometrodynamical Analysis to Characterize the Dynamics and Stability of a Molecular System through the Boundary of the Hill’s Region
Grupo de Sistemas Complejos, Departamento de Física y Mecánica, Escuela Técnica Superior de Ingenieros Agrónomos, Universidad Politécnica de Madrid, Madrid, Spain
Grupo de Sistemas Complejos, Departamento de Física y Mecánica, Escuela Técnica Superior de Ingenieros Agrónomos, Universidad Politécnica de Madrid, Madrid, Spain
Grupo de Sistemas Complejos, Departamento de Física y Mecánica, Escuela Técnica Superior de Ingenieros Agrónomos, Universidad Politécnica de Madrid, Madrid, Spain
Instituto de Ciencias Matemáticas (ICMAT), Madrid, Spain
Departamento de Química, Universidad Autónoma de Madrid, Madrid, Spain
- 1 Grupo de Sistemas Complejos, Departamento de Física y Mecánica, Escuela Técnica Superior de Ingenieros Agrónomos, Universidad Politécnica de Madrid, Madrid, Spain
- 2 Grupo de Sistemas Complejos, Departamento de Física y Mecánica, Escuela Técnica Superior de Ingenieros Agrónomos, Universidad Politécnica de Madrid, Madrid, Spain
- 3 Grupo de Sistemas Complejos, Departamento de Física y Mecánica, Escuela Técnica Superior de Ingenieros Agrónomos, Universidad Politécnica de Madrid, Madrid, Spain
- 4 Instituto de Ciencias Matemáticas (ICMAT), Madrid, Spain
- 5 Departamento de Química, Universidad Autónoma de Madrid, Madrid, Spain
Applied Mathematics·Volume 05 (2014)·Pages 2630–2642·Published 29 August 2014·DOI10.4236/am.2014.516251
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Abstract
In this paper we study the dynamics and stability of a two-dimensional model for the vibrations of the LiCN molecule making use of the Riemannian geometry via the Jacobi-Levi-Civita equations applied to the Jacobi metric. The Stability Geometrical Indicator for short times is calculated to locate regular and chaotic trajectories as the relative extrema of this indicator. Only trajectories with initial conditions at the boundary of the Hill’s region are considered to characterize the dynamics of the system. The importance of the curvature of this boundary for the stability of trajectories bouncing on it is also discussed.
KeywordsGeometrodynamical AnalysisMolecular Nonlinear DynamicsStability Geometrical IndicatorRiemannian GeometryHamiltonian Systems
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