TITLE:
Geometrodynamical Analysis to Characterize the Dynamics and Stability of a Molecular System through the Boundary of the Hill’s Region
AUTHORS:
Alberto Vergel, Rosa M. Benito, Juan C. Losada, Florentino Borondo
KEYWORDS:
Geometrodynamical Analysis, Molecular Nonlinear Dynamics, Stability Geometrical Indicator, Riemannian Geometry, Hamiltonian Systems
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.16,
September
19,
2014
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.