Lagrange points of the Euler solutions of the three body problem:

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We explain the classical Lagrange points. We explain the solutions of the 3-body problem found by Euler and then we explain the solutions of the restricted 4 body problem that move on concentric circles with the same angular velocity as the primary bodies (being the primaries any Euler solution of the 3-body problem)
  1. Oscar Perdomo
  2. Lagrange Points
  3. Euler solution of the 3 body problem
  4. Central configurations
  5. Restricted 4 body problem
  6. n body problem
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I have a very basic question at the very beginning - why do the masses move in sort of opposite directions? That is, the body at point (1, 0) moves counterclockwise while the body starting at (-r2, 0) moves clockwise in your given parameterization of their motions. It seems like this must be hugely significant to the results that follow - I think I just figured out the answer to my own question - that is needed to fix center of mass at the origin - thank you - your video provided some great insight for me on derivation of the Lagrange points

csvaughen