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I am curious about the naming and why were the equilibrium solutions of the CR3BP called as Libration points? Who called them that and what is the history behind it?

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This is a supplemental answer to @CallMeTom's answer.

Wikipedia's Lagrangian point; History says:

The three collinear Lagrange points (L1, L2, L3) were discovered by Leonhard Euler a few years before Joseph-Louis Lagrange discovered the remaining two3,4

3"KoLoMaRo" (Wang Sang Koon, Martin W. Lo, Jerrold E. Marsden and Shane D. Ross) Dynamical Systems, the Three-Body Problem, and Space Mission Design (also archived here and discussed in this answer)

4 written in Latin and math: De motu rectilineo, trium corporum se mutuo attrahentium

(with help from Latin SE)

I think "libration" comes from the behavior of the simplified linearized equations (sect. 2.6 of KoLoMaRo above where there is harmonic oscillatory motion, so an object near there would appear to oscillate back and forth, or librate. More detailed analysis will show some of these to be stable and others unstable. An object in a Lissajous or halo orbit will oscillate for a while (for Sun-Earth system perhaps several periods or a few years) but drift away over time and finally do something weird.

Interestingly former NASA engineer, flight director and Space Shuttle program manager, Wayne Hale's October 2019 blog post Definition of Terms covers this very question, and seems to disagree with this viewpoint!

I recommend reading the full post for sure, but to summarize the post shows some "libration points" of the Moon, where lunar libration is maximum.

The spot on the edge of the moon that is tilted the most toward an earthly observer is called ‘the libration point’.

Have you heard that term before? I bet you have but in a different context.

Joseph-Louis Lagrange (1736-1813) was an Italian mathematician who played a large part in the development of the metric measurement system (SI) in post-revolutionary France. He also studied orbital mechanics involving three bodies (e.g. sun/earth/moon) and mathematically proved there are locations around such an orbit which are gravitationally stable. These points are called Lagrange points in his honor. There are typically 5 such points and I will leave it to the student to research their locations.

As you can see Lagrange points and Libration points are quite different and literally have nothing to do with each other.

But if you read any number of popular media stories – and even several NASA technical papers – there appears to be confusion and the terms are used interchangeably. This is so widespread that some dictionaries have started changing the definitions to keep up with what appears to be popular usage.

STOP THAT!

Unfortunately, the curmudgeon in me realizes that this erroneous usage has become so common that it will be hard to change usage in popular literature.

But at least you now know the difference. And you, like me, will stop when you hear some ‘expert’ (never an astronomer) mixes the terms and think about how much ignorance is being displayed.

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"Libration" comes from latin "librare" and means "to keep balance". And this is because in a three-body problem objects keep balance in this points. I do not know who named it "Libration Points" first, I would assume LaGrange or Euler. I would even assume: they have been first called "libration points" and later "LaGrange Points".

Nethertheless: both means the same:

Lagrangian Point WIKIPEDIA

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