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Torque-Free Rigid Body: Euler's Equations 3D

A Phong-shaded inertia ellipsoid tumbles under Euler's torque-free equations, integrated with RK4 and a unit quaternion. The angular-velocity vector traces the polhode on the body and the herpolhode in space while the angular momentum stays fixed. Spinning about the intermediate principal axis triggers the Dzhanibekov (tennis-racket) flip.

Figure 1. Torque-free rigid-body rotation; polhode and herpolhode of the angular-velocity vector.

WHAT TO TRY

  • Vary each control and watch the rail readouts respond.
  • Compare the diagnostic plot against the live scene.