After getting the basic propagator working, I moved on to the next thing I needed for Gateway Navigator: the State Transition Matrix (STM).
At first I thought this would be fairly straightforward. The idea seemed simple enough — propagate the spacecraft state and also keep track of how small changes in the initial state affect the state later on. In practice, it was a lot more annoying than I expected.
I started by going through the CR3BP equations again and deriving the Jacobian of the dynamics. The main problem was keeping track of all the partial derivatives without making a sign mistake. Since the rotating-frame equations already contain the Coriolis terms, it was surprisingly easy to convince myself that an incorrect expression was correct.
I implemented the variational equations and augmented the spacecraft state with the 36 STM elements. The first propagation technically ran, but the STM results were clearly wrong. Some elements were growing far too quickly and the numerical behaviour didn’t make physical sense.