Orbital mechanics question DSCOVER L1 orbit

In article , says...

If it is this complex, would one expect that keeping a craft in this point
is goind to use more fuel?

Depends on the details of the "halo orbit" that it is in. Yes, halo
orbits are complex and are very weird since they're not a circular path
and there is no mass at the "center" of the point it is orbiting. But
if you do it right, it doesn't take much delta-V to stay in a "halo
orbit".

It seems to me that we are dealing with some very complex forces
here and although the tendency is for things to stay there, any
other forces woould not need to be that poweful to make it come
out of the point and start behaving differently.

This is why Orbital Mechanics was one of the hardest 500 level classes I
took at Purdue. Spacecraft Attitude Dynamics was the other 500 level
class that was quite difficult. Lots of math. Lots of derivations.
Lots of simplifications that you can't completely ignore in the real
world.

Jeff
--
"the perennial claim that hypersonic airbreathing propulsion would
magically make space launch cheaper is nonsense -- LOX is much cheaper
than advanced airbreathing engines, and so are the tanks to put it in
and the extra thrust to carry it." - Henry Spencer