Trojan asteroids orbit the Sun in resonance with Jupiter at Lagrange points, and have their own stable orbits about these points. This can be treated as a restricted three-body problem, which is numerically evaluated in this report using a stiff Radau method to solve the system of coupled differential equations. I simulate the maximal deviation from the Lagrange points (in the rotating frame) without perturbations, to demonstrate the stability of these points. Under small perturbations, I also demonstrate the predicted existence of stable tadpole and horseshoe orbits.
A list of the content of each file can be found in the 'program_structure.txt' file. The final report (and high resolution copies of the graphics included within) is given in the Figures file.