Orbits are considered in conventional stellarators (i.e. with helical coils) using Boozer co-ordinates. The Advanced Toroidal Facility (ATF) in Oak Ridge, Tennessee, will be used as an example to study the effects of its configurational flexibility on orbit topology. It is shown that the symplectic integration technique yields superior results for single particle orbits. These orbits will be compared with predictions using the J* invariant. J* conservation allows examination and understanding of the global stellarator topology, both with and without radial electric fields