  We consider the nature of orbits near the solar neighborhood which are
perturbed by local spiral arms and the Milky Way bar. We present a simplified
Hamiltonian model which includes resonant terms from both types of
perturbations and is similar to the forced pendulum. Via numerical integration
of this model we construct Poincare maps to illustrate the nature and stability
of the phase space. We find that resonance overlap is most likely to cause
widespread chaos when the pattern of the spiral structure puts the solar
neighborhood near the 2:1 inner Lindblad resonance (ILR) in the case of a
2-armed pattern, or near the 4:1 ILR in the case of a 4-armed pattern. When
this happens both the quasiperiodic orbits which support the spiral structure
and those that oscillate with the bar are disrupted near the bar's 2:1 outer
Lindblad resonance (OLR). Consequently the pattern speed of spiral structure
which passes through the OLR must be faster than 0.45 times the solar
neighborhood angular rotation rate if it is 2-armed or faster than 0.75 times
this value if it is 4-armed. Alternatively the OLR may form a boundary between
spiral modes at different pattern speeds. In all cases we find that spiral
structure is disrupted by the OLR over a narrow range of radius and the extent
of the orbits aligned perpendicular to the bar at the OLR is limited by the
spiral perturbations.
