Author(s)

Alberto Vergel¹, Rosa M. Benito¹, Juan C. Losada¹, Florentino Borondo²

¹Grupo de Sistemas Complejos, Departamento de Física y Mecánica, Escuela Técnica Superior de Ingenieros Agrónomos, Universidad Politécnica de Madrid, Madrid, Spain.
²Instituto de Ciencias Matemáticas (ICMAT), Madrid, Spain.
³Departamento de Química, Universidad Autónoma de Madrid, Madrid, Spain.

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.

Geometrodynamical Analysis, Molecular Nonlinear Dynamics, Stability Geometrical Indicator, Riemannian Geometry, Hamiltonian Systems

Vergel, A. , Benito, R. , Losada, J. and Borondo, F. (2014) Geometrodynamical Analysis to Characterize the Dynamics and Stability of a Molecular System through the Boundary of the Hill’s Region. Applied Mathematics, 5, 2630-2642. doi: 10.4236/am.2014.516251.