Document Type

Thesis

Degree Name

Master of Science (MSc)

Department

Mathematics

Program Name/Specialization

Mathematics for Science and Finance

Faculty/School

Faculty of Science

First Advisor

Dr. Cristina Stoica

Advisor Role

Supervisor

Abstract

In this thesis we study relative equilibria of di-atomic and isosceles tri-atomic molecules in classical approximations with repulsive-attractive interaction. For di-atomic systems we retrieve well-known results. The main contribution consists of the study of the existence and stability of relative equilibria in a three-atom system formed by two identical atoms of mass $m$ and a third of mass $m_3$, constrained in an isosceles configuration at all times.

Given the shape of the binary potential only, we discuss the existence of equilibria and relative equilibria. We represent the results in the form of energy-momentum diagrams. We find that fixing the masses and varying the potential defining parameters could lead to no spatial, one family of spatial, or two families of spatial relative equilibria. We also observe that varying the value of $m$ leads to a shift in the relative equilibria, and that varying $m_3$ has no effect on the existence of relative equilibria, but may change their stability. We specialize the existence results to Lennard-Jones models and further study stability by performing numerical experiments.

Convocation Year

2014

Convocation Season

Fall