Does anyone have a reference to a rigorous stability analysis for the L4
and L5 Lagrange points?
Here's what I (think I) know:
In the rotating frame, L4 and L5 are actually local maxima of
the combined gravitational and centrifugal potential.
Thus, the stability is critically dependent upon the action of
the Coriolis force.
These points are stable iff the ratio r of the masses of the two
primary bodies exceeds about 25.
The number 25 is apparently the solution of the equation
(1 + r)^2 = 27r
It had occurred to me to try the following:
Consider a particle that is given an infinitesimal shove away
from the Lagrange point. Find its speed at any later position
based on conservation of energy in the combined gravitational
and centrifugal potential function. Calculate the resulting
magnitude of the Coriolis force. Under the assumption that the
particle is moving in such a way that the Coriolis force is
directed "inward" toward the Lagrange point, see if its
magnitude is at least large enough to sustain orbital motion
around that point despite the net "outward" gravitational and
centrifugal force. Unfortunately, my results would seem to
indicate that the point is stable for any value of r.
So my question really is
Am I on the right track?
If so, where might I have gone wrong and if not, how *does* one
do this kind of stability analysis?
Where does the equation for r come from?
Is the analysis perfectly rigorous or is it more of a
plausibility argument? (Like mine.)