Garmaine Staff asked 2 years ago

The paper Earth-Moon Near Rectilinear Halo and Butterfly Orbits for Lunar Surface Exploration (AAS 18-406) says

Periodic Orbits in the Earth-Moon System

The current investigation focuses on three types of periodic orbits in the vicinity of the Moon: Near Rectilinear Halo Orbits (NRHOs), which are periodic in the Earth-Moon rotating frame in the CR3BP; butterfly orbits, a periodic family that bifurcates off the NRHOs; and circular Low Lunar Orbits (LLOs), which are periodic in a Keplerian sense.

and shows the drawing below. There are several questions and answers here about near-rectilinear halo orbits and the ever-so-popular YouTube video Near Rectilinear Halo Orbit Explained and Visualized Okay, I like it at least.

But I can't understand nor visualize what these butterfly orbits look like in 3D or how objects move in them. Is it possible to generate one and show it here with a few views, or to find a resource where this is done, or even to just provide an algorithm and a python script that makes them? Even a set of initial state vectors would be enough to get started.

Figure 1: L2 Family of NRHOs and Butterflies

Figure 1: L2 Family of NRHOs and Butterflies