Trajectories with Prescribed Itineraries in the Three-Body Problem - MATLAB Tutorial

Learn how to find trajectories with prescribed itineraries in the planar circular restricted three-body problem through this comprehensive tutorial and MATLAB demonstration. Explore numerical methods for generating periodic orbits and their invariant manifolds, focusing on an algorithm to create trajectories with specific itineraries. Follow along with a detailed example computation in MATLAB, demonstrating how to take a Poincaré section of a stable manifold tube on a Lagrangian L1 Lyapunov orbit. Gain insights into differential correction techniques, the use of state transition matrices, and the step-by-step process of constructing complex orbital trajectories. Download the provided MATLAB code to execute the examples and deepen your understanding of advanced orbital dynamics concepts.

Introduction, Summary
Find region with desired itinerary for trajectory
Step 1, Select appropriate energy
Step 2, Compute Lagrange point eigenvalues & eigenvectors
Step 3, Compute Lyapunov orbits via numerical continuation
Matlab tutorial begins, code provided see link above
Step 4, Compute stable and unstable invariant manifold tubes
Step 5, Poincare section of tube
Step 6, Compute other tube Poincare sections
Step 7, Pick initial condition in intersection of tubes X,J,S
Tube intersection after several circuits about secondary mass
Temporarily captured satellite of Jupiter
Longer itinerary construction X,J,S,J,X