Halo orbits construction based on invariant manifold technique.

The current investigation applied the invariant manifold technique to study the halo orbits around the libration points in circular restricted three-body problem. Two dominant (leading) directions were considered as dominant motions for the construction of spatial halo orbits, the third direction motion being the slave (following) motion. The dominant motions correspond to four-dimensional invariant manifolds in the phase space. The invariant nonlinear asymptotic relations (i.e. INARs) between the two dominant motions and the slave motion were established, enabling a transformation from the 3-DOF problem into a 2-DOF problem. Application of the INARs are also discussed. Such invariant nonlinear relations in polynomial expansion form could be used as: (I) approximate analytical solutions; (II) topological constraints to obtain more exact numerical solutions with differential correction. General findings in the current research revealed that the nonlinear asymptotic relations among the directions provided an alternative point of view to explore the overall dynamics of halo orbits around libration points with general rules. The effectiveness of the proposed method was also verified by numerical simulations. • Invariant nonlinear asymptotic relations (INARs) between dominant and slave motions are obtained. • The 3D system is reduced into a 2D system by INARs. • Analytical solutions for halo orbits are obtained by INARs. • INARs are used as topological constraints to obtain halo orbit with differential correction. [ABSTRACT FROM AUTHOR]