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.
Recommended Citation
McKinley, Damaris Miriam, "Relative Equilibria of Isosceles Triatomic Molecules in Classical Approximation" (2014). Theses and Dissertations (Comprehensive). 1686.
https://scholars.wlu.ca/etd/1686
Convocation Year
2014
Convocation Season
Fall
Included in
Chemistry Commons, Dynamical Systems Commons, Non-linear Dynamics Commons, Numerical Analysis and Computation Commons, Ordinary Differential Equations and Applied Dynamics Commons, Physics Commons