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Your Universe of Digital Possibilities
A rigid body thrown spinning into empty space keeps its angular momentum and its energy forever — two numbers fixed for all time. And yet a spin about the middle of its three axes will not hold: the body flips end over end, unbidden, then flips back, on a clock no one wound. It looks like something is pushing it. Nothing is. The somersault is the only motion that keeps both conserved quantities exactly — geometry, not force, wearing the mask of chaos.
In the body frame, with no torque, the spin obeys three coupled equations. The sign of (I2 − I3) and its cyclic kin decides whether a small wobble decays or grows.
Angular momentum and energy are both conserved; in ω-space one is a sphere, the other an ellipsoid, and the motion must ride their intersection — the polhodeof Poinsot’s rolling construction.
Spin about the largest or smallest principal axis is stable; spin about the middle one is not — the body flips 180° over and over, the Dzhanibekov effect filmed on a wing-nut in orbit.
The two conserved quantities are a sphere (|L|² fixed) and an ellipsoid (2T fixed) in the space of ω; the body’s spin must ride their intersection — the polhode. About the largest or smallest axis those curves are tight closed loops, so ω barely wanders. About the middle axis the intersection is an X whose crossing runs through the spin pole, so the slightest nudge sends ω the long way around — the flip. It is the same lesson as The Knot and The Soliton: a conserved shape can still rearrange, and what looks like chaos (The Arrow’s territory) is here pure, reversible geometry.