Lagrange Points are special locations in planetary systems where gravitational and rotational forces cancel out. Sometimes we find asteroids or dust clouds lingering near these places. Space missions may use some of these locations for spacecraft as they offer many advantages over orbiting in the Earth directly.

Universe Sandbox is used for some of the 3 body problem animations
https://universesandbox.com/

Other graphics are created with GMAT and POV Ray

For a more mathematical derivation of these check out this series:
   • Lectures on Halo Orbits  

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