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L1, L2, and L3 are unstable -- as you say, they're saddle points, which is to say they're stable in one direction but unstable in the other.
L4 and L5 are stable (metastable, because a large enough disturbance can toss you out of them).
As for orbital mechanics, it's easy:
East takes you out
Out takes you west
West takes you in
In takes you east
North and south bring you back
-- Larry Niven, _The Smoke Ring_
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