Halo Orbit Manifold Tubes — Planar Saddle Phase Portrait (2D)

This 2D companion integrates the exact same nonlinear restricted three-body equations of motion as the 3D halo-orbit simulator, restricted to the planar invariant slice (z = 0) where the saddle instability actually lives — the out-of-plane halo motion is a separate, decoupled oscillator that never drives the instability. Instead of a rotating 3D camera, it shows the synodic (x,y) plane directly and a log-scale growth chart tracking measured manifold-tube displacement against the linear-theory prediction e^λt, so you can see both the instability and the honest limits of the local eigenvector approximation used to seed it.