Halo Orbit Manifold Tubes

Spacecraft parked near the Sun-Earth L1 or L2 Lagrange point don't sit still — they fly halo or Lissajous orbits built from the point's two oscillatory (center) modes, while a third, real saddle mode makes the whole neighborhood exponentially unstable. This simulator integrates the full nonlinear restricted three-body equations of motion to render that orbit, then launches swarms of nearby trajectories along the local stable and unstable eigendirections so you can watch the invariant-manifold tubes form — the unstable tube shows why real missions need periodic station-keeping burns, and the stable tube shows the near-zero-fuel corridor mission designers ride in.