As an example of a very low friction system, Monte Carlo Brownian dynamics simulations have been used to calculate equilibrium structures of a polyelectrolyte brush grafted onto planes. The polymers were calculated in a semi-flexible coarse-grain model that is appropriate to treat the charge density of the polyion. The effect of linear charge density on the polyion $\xi$, the surface negative charge, and added salts were studied. In salt-free solution, scaling theories predicted the structure well in the low $\xi$ region. In the high $\xi$ region, additional shrinkage was found from the theories due to counterion condensation. The effect of surface charge showed not only the repulsion of the polyion from the surface but also the shrinkage in the high $\xi$ region due to the additional counterions required for electrical neutrality. The addition of salts led to the shrinkage of the brush heights, and in the high $\xi$ region, additional extension was found. The computational strategy for calculating the friction dynamics of the system is also discussed.