Regular and stochastic behavior in single particle orbits in static magnetic reversals have wide application in laboratory and physical plasmas. In a simple magnetic reversal, the system has three degrees of freedom but only two global (exact) constants of the motion, the system is nonintegrable and the particle motion can, under certain conditions, exhibit chaotic behavior. Here, we consider the dynamics when a constant shear field is added. In this case, the form of the potential changes from quadratic to velocity dependent. We use numerically integrated trajectories to show that the effect of the shear field is to break the symmetry of the system so that the topology of the invariant tori of regular orbits is changed. In this case, invariant tori take the form of nested Moebius strips in the presence of the shear field. The route to chaos is via bifurcation (period doubling) of the Moebius strip tori.