Extended-body effects in general relativity: What is possible?

Abstract: To a first approximation, objects in general relativity move along geodesics. But this is not exact. A body's internal structure can affect its motion. What does that allow? I will talk about a case where a spacecraft can actively control its internal structure, and in that case, extended-body effects can be used to control an orbit without the use of a rocket. Unstable orbits can be stabilized, bound orbits can be made unbound, and more.