Gravitational sling shot - with magnets

[Onevoice]

I thought of this while driving my smog generator to work this morning. Magnetic fields and gravitational fields both share a symmetry which implies that you cannot get energy out of the system greater than the energy put in, but in the case of gravity, you can perform maneuvers to slingshot space probes to outer planets that both shortens the travel time and allows for much less fuel use. Now imagine a Kepler rosette. Several bodies in orbit at the same distance from their center. You could, hypothetically, plot a course for a satelite to travel from planet to planet to planet without using any fuel (except for course corrections). Shouldn't it be possible to translate this hypothetical course into a small scale rotor\stator design that would duplicate the same behaviour. Shouldn't it be possible to extract energy out of this system...