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If two bodies move in circular orbits about their common centre of mass and the mass of the third body is too small to affect the motion of the other two bodies, the problem of the motion of the third body is called circular restricted three-body problem (CR3BP). This system has five equilibrium points which is known as Lagrangian points. Among five equilibrium points, L4 and L5 Lagrangian points are stable while L1, L2 and L3 are unstable. In this paper, we consider the motion in the vicinity of the L4,5 Lagrangian points where the implicit control structure provides an insight into the control structure underlying the problem.

Implicit Control Structure in Lagrangian Points of Circular-restricted Three-body Problem