I started reading about rotational dynamics because a GPU kernel involved coordinate transforms. I stayed because the math is beautiful and deeply unintuitive.
What spins isn't what you think. A rigid body rotating about an axis doesn't just "spin around that axis." The angular momentum vector points in a different direction than the angular velocity vector — unless you're rotating about a principal axis. The moment of inertia is a tensor, not a scalar, and it transforms with the body's orientation.
The intermediate axis theorem. Spin a tennis racket about the axis through the handle (long axis) — stable. Spin it about the axis perpendicular to the strings (short axis) — stable. Spin it about the intermediate axis (through the side of the head) — it flips. Every rotation. No amount of careful throwing fixes it. The Dzhanibekov effect, verified on the ISS: a spinning wingnut flips periodically. The intermediate axis is unstable because the moments of inertia create a saddle point in the phase space.
Why this matters for computing. Quaternion slerp for smooth camera rotations, rigid body simulation for physics engines, and orientation estimation from IMU data all depend on understanding rotational dynamics. A naive Euler-angle interpolation drifts; a quaternion slerp stays on the unit sphere. But the deeper truth: you can't understand quaternions unless you understand the rotation group SO(3), and you can't understand SO(3) unless you understand why spinning things resist being tipped.
The GPU kernel I was debugging turned out to be fine. I'd made an error in the coordinate transform — a 90-degree rotation that should have been -90. But the rabbit hole was worth it.