Are there propellant-less ways to balance at an unstable orbital point?

Question

A station situated somewhere like EML-2 is really at an unstable point. I've heard of crafts using rocket firing to maintain that position in response to small deviations. Could you do this without using propellant?

I wonder if this could be done by moving a long pole back and fourth, like a tightrope walker.

Answer 1

No, unless you have a rather massive and long pole. To be in a stable orbit, your center of mass¹ must be at a particular point with a particular velocity. Rearranging your own mass without expelling any will not work as you cannot move your own center of mass.

However, with a long enough pole, the inverse square effects come into play, so one can change the net gravitational attraction by moving a pole back and forth, and thus regain the orbit.

^{1. The mass distribution will change your rotational properties, but not the revolutionary ones which depend on the position and velocity of the COM, assuming a near-homogeneous gravity field..}