Is there a way to calculate the libration amplitude of a test object that orbits the $L_4$ or $L_5$ Lagrange points?
By amplitude I mean the distance along the orbit between the two extremes of libration. I.e. the point in the tadpole orbit (as examined in a co-rotating frame) where the orbiting test object is farthest from the planet, and then the point at the other extreme where the test object most closely approaches the planet before turning back toward the $L_5$ (or $L_4$).
Without working out any equations, on the surface it seems that the amplitude (as well as whether the object is in a tadpole or horseshoe orbit) will depend on the energy the test object has when it is captured. Is that a safe assumption?