Quadrotor Phase 1: hand-written physics, RK4 first

Phase 1 of the quadrotor sim is physics plus a bare renderer, and I decided to work through the theory before writing any of it. That started with RK4 — a Wikipedia-level foundation first, then deep enough to write the integrator myself and know why each stage exists.

With the foundations in place, I wrote the physics functions by hand. Plenty of it was autocompleted along the way, but I went through every line to make sure I understood it and that it was correct, then passed the code through a review pass before accepting it. The scaffolding, CMake setup, and rendering work is where I lean on AI assistance — the equations of motion and the integration math stay mine.

Architecture decisions locked this session: the sim plane is XZ (+X right, +Z up), theta = 0 is level hover with positive counter-clockwise, state is [x, z, theta, xdot, zdot, thetadot] as an Eigen 6-vector, inputs are two raw rotor thrusts in Newtons, and integration is fixed-timestep RK4.

One process lesson worth recording: commit your own work before letting the AI touch it. I let edits land on top of uncommitted physics code this session, which muddied the history — from here on, my code gets committed first, then generated changes land as their own commits.

Next up: a basic renderer with the state vector on screen and a rigidbody visibly moving through the scene. Then Phase 2 — control.