Stability of L points

>
> Another example is O'Neill's mass catcher at the Earth-moon L2
point. The
> constant impact of incoming ore displaces the catcher, but it always
tends
> to return. But on the other hand, all it takes is a very modest
thrust
> either toward or away from the moon to easily slip off the point.
>
> Wendell Mendell has made an argument for a spaceport at the
Earth-moon L1
> point. The ease with which one could push off either toward the
Earth or
> the moon made it an obvious way station to him. Also, if one was
staging
> there for a mission to Mars, say, it would be very easy to slip off
that
> point toward the Earth, whip around with engines thrusting, and thus
enjoy a
> significant kinetic energy advantage.
>

You are visualizing correctly, but calling it the wrong thing. draw a
line between Earth and the moon. That is the radial direction. This is
the direction that is unstable. The two directions perpendicular are
the tangential directions.

Bill