  The energy spectrum of the baryons is determined by treating each of them as
a three-body system with the interacting forces coming from a set of two-body
potentials that depend on both the distance between the quarks and the spin and
orbital angular momentum coupling terms. Constraint dynamics is first reviewed
for a relativistic two-body system in order to assemble the necessary two body
framework for the three-body problem and then we review the different types of
covariant two-body interactions involved in constraint dynamics, including
vector and scalar, and solve the problem of energy eigenstates using constraint
dynamics. The Two Body Dirac equations of constraint dynamics derived by Crater
and Van Alstine, matched with the quasipotential formalism of Todorov as the
underlying two-body formalism are used, as well as the three-body constraint
formalism of Sazdjian to integrate the three two-body equations into a single
relativistically covariant three body equation for the bound state energies.
The results are analyzed and compared to experiment using a best fit method and
several different algorithms, including a gradient approach, and Monte Carlo
method.
