For my ME314 class this past spring, we had to simulate a dynamical system in Python. I chose to do one of my prized possessions, the Lego NASA SLS Technic set.

I wrote the code for the entire project, from setting up the Euler-Lagrange Equations, to implementing collision checks and impact updates, to the numerical simulation and the final animation. Guidance and feedback was received from Professor Todd Murphey.

For this simulation, I considered three independent bodies: the Core, the Orion capsule, and the boosters (I analyzed one booster and then mirrored the results about the y-axis for the second booster).

I also considered a couple different phases of flight:

Stage 1: Core, boosters, and Orion all rising together. Boosters and Orion are constrained to stay attached to the core.

Stage 1.5: Boosters stop firing, are still constrained to the core. This stage should last a very short time as it will be used to decide when the boosters detach.

Stage 2: External force on boosters starts again (reasons discussed below). Boosters are constrained to follow parabolic trajectory and turn (the x-position and angle from the vertical of the booster are constrained as a function of the booster’s height). Core and Orion continue rising together.

Stage 2.5: Core stops firing, Orion still attached. This stage should last a very short time as it will be used to decide when Orion detaches. Booster external force also shuts off and they enter free-fall.

Stage 3: Orion continues rising (under its own engine power), boosters and core in free-fall. System is checking for when the core hits the ground.

Stage 4: Core hits the ground. Orion continues rising and boosters continue falling.