The fast Lyapunov indicator (FLI), related to better known maximum Lyapunov exponent (MLE), has been applied to individual asteroids, symplectic maps, and the circular restricted three-body problem. In the circular restricted three-body problem FLI maps have been used to expose invariant manifolds connecting resonant islands in the Jupiter-Europa system. Similar structures exist on a variety of length and time scales throughout the solar system providing dynamical pathways for the transport of both natural and man-made objects. This paper discusses the practical and theoretical details of applying stability mapping in conjunction with manifold seeding, collision mapping, and the inclusion of dissipation. A mapping technique is presented that facilitates the construction of non-collision orbits into and out of the distant retrograde region. Application to the Sun-Jupiter system demonstrates heteroclinic connections responsible for satellite capture into the distant retrograde orbits. Capture regions are identified in both the conservative and dissipative systems. In the field of astrodynamics, these techniques can be used to construct insertion trajectories into energetic, stable distant retrograde orbits.