| Abstract: |
| Consider the spatial restricted three-body problem, as a model for the motion of a spacecraft relative to the Sun-Earth system. We focus on the dynamics near the equilibrium point $L_1$, located between the Sun and the Earth. We show that we can make the spacecraft transition from an orbit that is nearly planar relative to the ecliptic, to an orbit that has large inclination, at zero energy cost. (In fact, the final orbit has the maximum inclination that can be obtained through the particular mechanism that we consider.
Moreover, the transition can be made through any prescribed sequence of inclinations in between).
We provide several explicit constructions of such orbits, and also develop an algorithm to design orbits that achieve the \emph{shortest transition time} for this particular mechanism.
Our main new tool is the `Standard Scattering Map` (SSM), a series representation of the exact scattering map. The SSM can be used in many other situations, from Arnold diffusion problems to transport phenomena in applications. |
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