On 26/10/12 22:53, Dr J R Stockton wrote:
It is easy enough to state, without proof that (and roughly where) L1 L2
L3 exist, and are unstable as is a ball on the nose of a seal; and that
L4 L5 exist, and are stable as is a ball on the inside of a wok.

Easy to state, but wrong; eg, in the restricted circular
problem, L4 and L5 are stable only if 27PS (P+S)^2, where P and
S are the masses of primary and secondary; even then, it's more
like rolling around on an upturned wok [ie, "naturally" unstable],
but with the wok being twisted around so as to keep the ball up.
[Proof beyond the scope of this article, and just about at the
limits of undergraduate mechanics, I'd guess.]

--
Andy Walker,
Nottingham.