  An analytic resolution of the covariant oscillator quark model for a
three-body system is presented. Our harmonic potential is a general quadratic
potential which can simulate both a $\delta$-shape configuration or a
simplified Y-configuration where the junction is located at the center of mass.
The mass formulas obtained are used to compute glueball and baryon spectra. We
show that the agreement with lattice and experimental data is correct if the
Casimir scaling hypothesis is assumed. It is also argued that our model is
compatible with pomeron and odderon approaches.
