(a) Make your own version of Figures 3.7 and 3.9, including contours of the Jacobi constant, the locations of the two masses, the locations of L1 to L5, and the unit circle.
(b) Use rebound to simulate tadpole and horseshoe orbits and reproduce as best you can Figures 3.16 and 3.17. Note that the initial conditions are given in the figure captions.
For each one, also plot
and of the test particle as a function of time (as in Fig 3.19),
the Jacobi constant and the Tisserand relation (Eq. 3.46) as a function of time to check that they are indeed constant,
against (as in Fig 3.18).