Collective Behavior can start to be modeled in two modes, the Lagrangian or Eulerian.
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Lagrangian points are the locations in space where
the combined gravitational pull of two large masses roughly balance each other.
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In addition, the range of allowable
coordinate transformations is much wider than in Lagrangian mechanics, which makes it even easier to find movement integrals
and conserved quantities.
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Along with its moons, Jupiter's gravitational field controls
numerous asteroids that have settled into the regions of the Lagrangian points preceding and following Jupiter in its orbit around the Sun.