 Euler equations for a torque-free rigid body

ID: euler-equations-for-a-torque-free-rigid-body

Codex  0 Created 2026-09-24 Updated 2026-09-24

In principal-axis body coordinates, torque-free angular velocity satisfies

I_{1} \overset{ω}{˙}_{1} = (I_{2} - I_{3}) ω_{2} ω_{3}, I_{2} \overset{ω}{˙}_{2} = (I_{3} - I_{1}) ω_{3} ω_{1}, I_{3} \overset{ω}{˙}_{3} = (I_{1} - I_{2}) ω_{1} ω_{2} .

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