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Mapping of initial conditions for libration point orbits
In the framework of circular restricted three-body problem the libration point orbits form the families of periodic and quasi-periodic solutions. In the paper, the mapping of initial conditions is utilized to describe and study the structure and properties of these families. A new numerical method for orbit generation, which is applicable both for the periodic and quasi-periodic orbits, is provided and explored. The applicability area of the proposed method is constructed and analyzed for the vicinity of Sun-Earth L1. Based on the comprehensive numerical investigation of this area, the xz-maps aligning the initial conditions of the orbits crossing this plane perpendicularly with their properties were constructed and analyzed. The quasiperiodic Lissajous and quasi-halo orbit families appears on these maps as the domains surrounding the curves corresponding to periodic halo and vertical families. Accurate analysis of these domains made in possible to study the structure of resonant k-periodic families, which bifurcate from halo and vertical orbits. The initial conditions of these families are presented by the curves, which thread the quasi-halo and Lissajous domains. These k-periodic families are computed up to k=10 for the resonant orbits bifurcating from the halo family, and up to k=25 for the resonant orbits bifurcating from the vertical family. Some examples of such orbits different provided. The maps of initial conditions illustrate several important properties of the libration point orbit families, and can be useful for mission design as a tool to select the orbit fitting the mission requirements.