The libration points are of great interest for applications and so their stability was a subject of many papers during the past two hundred years.
Obviously, the particle [P.sub.2] may be situated in any of the five equilibrium positions of the corresponding three-body problem which coincide with the libration points [L.sub.1], ..., [L.sub.5] in case of [m.sub.2] =0.
To complete the study of the equilibrium positions in the restricted fourbody problem one needs to consider the case when particle [P.sub.2] is situated in one of the collinear libration points [L.sub.1], [L.sub.2], [L.sub.3] and, therefore, the massive particles [P.sub.0], [P.sub.1], [P.sub.2] are located on the same straight line.
The deployment of spacecraft formation in libration points orbit can be achieved for long baseline interferometry, which is of great significance to the study of the origin of the universe.
According to these parameters we can obtain simulation curves through control method of keeping flight formation by using SDRE on the sun-earth libration points.
In 2005, Hill suggested placing navigation constellation on the periodic orbits in the vicinity of libration points of the Earth-Moon system to support deep space navigation .
Liu, "On motions around the collinear libration points in the elliptic restricted three-body problem," Monthly Notices of the Royal Astronomical Society, vol.
There are the hyperbolic equilibria which have stable, unstable, and centre manifolds for hyperbolic Hamiltonian system, just like the collinear libration points [L.sub.1], [L.sub.2], and [L.sub.3] in CR3BP , of which the unstable manifolds may cause instability in the Lyapunov sense.
For a hyperbolic Hamiltonian system, there exist hyperbolic equilibria that have stable, unstable, and center manifolds , which are similar to the collinear libration points [L.sub.1], [L.sub.2], and [L.sub.3] in CR3BP.
NASA is considering missions beyond low Earth orbit such as libration points
, which are gravitationally stable spots in space.
The existence of the libration points and their stability in the radiational elliptical restricted three-body problem has been investigated .
Tkhai, "Instability of libration points and resonance phenomena in the photogravitational elliptic restricted three-body problem," Solar System Research, vol.