i.e. with low energy/fuel requirements. SMD usually involves the approximation of the circular restricted problem of three bodies, say, for instance Sun-Earth-Spacecraft or Earth-Moon-Spacecraft systems, depending on current application.

There are five equilibrium points in an orbital configuration of two large bodies (in our case the Earth and the Moon), where the forces of gravity balance out; these are the Lagrangian points. There are five such points, labelled $L_1$ to $L_5$. The $L_1$, $L_2$ and $L_3$ (collinear) points are unstable, the $L_4$ and $L_5$ (triangular) points are linearly stable equilibrium points. The presence of a third large body, the Sun, destroys the stability of the Earth-Moon $L_4$ and $L_5$ points, but even though these points ($L_4$ and $L_5$) are unstable, there are bounded regions around these points for either shorter or longer periods of time.

Although the attention in space manifold dynamics has been focused mainly in collinear points $L_1$, $L_2$, and $L_3$ because of their unstable nature (Celletti & Giorgili 1991) and vicinity to the Earth ($L_1$, $L_2$). It can also be shown that escape from the vicinity of a natively stable libration point (e.g. $L_4$ or $L_5$ in the circular restricted three body problem (CRTBP)) is also governed 