Pseudo-Arclength Continuation of Halo Orbit Families Demo

Demonstrates how to use pseudo-arclength continuation to generate families of halo orbits about L1 and L2 in the CR3BP

Generating Earth–Moon L1/L2 Halo Orbit Families via Continuation

These example scripts demonstrate how to generate and visualize families of Earth–Moon L1 and L2 halo orbits using the psuedo-arclength continuation method implemented in the Pumpkyn CR3BP Toolbox.

Each demo:

• Initializes a small-amplitude halo orbit near the L1 or L2 Lagrange point
• Refines the orbit to achieve periodic closure using pumpkyn.cr3bp.cont
• Continuously varies the orbit amplitude via pseudo-arclength continuation
• Colors each trajectory by Jacobi constant
• Terminates when the orbit’s perilune intersects the lunar surface

Usage:

L1HaloDemo();
L2HaloDemo();

Outputs:

• 3D visualization of halo orbit families in the rotating Earth–Moon frame
• Colorbar keyed by Jacobi constant
• Mirrored orbits about the x–y plane (northern and southern branches)

Dependencies:

Requires the pumpkyn.cr3bp module — specifically the functions cont, jacobi, lagrangePts, and orbitProperties, which are included in the Pumpkyn Toolbox.

Educational and Mission Design Relevance

Halo orbits around L1 and L2 are foundational to cislunar mission design and have been used by missions such as JWST, ARTEMIS, and Gateway.

These demos illustrate how nonlinear dynamics and continuation methods can be used to map out entire families of periodic solutions — an essential step in designing transfer trajectories, relay constellations, and station-keeping strategies in the Circular Restricted Three-Body Problem (CR3BP).