General Physics I · Lecture 14

Rigid-body rotation

One motion, seen in physical space and angular-momentum space.

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Physical space

The body turns; angular momentum L stays fixed.

Fixed Le₁, e₂, e₃: body axesDrag to orbit

Angular-momentum space

Components L₁, L₂, L₃ measured along the rotating body axes.

SphereEnergy ellipsoidIntersection
t = 0.0|L| = 1.000E = 0.167

Changing a moment or the initial state starts a new torque-free motion. Slider limits keep the moments consistent with a physical rigid body.

Rotation near the intermediate axis

A small initial tilt grows. Watch the body flip while its angular momentum remains fixed in space.

L₁² + L₂² + L₃² = L²L₁²/(2λ₁) + L₂²/(2λ₂) + L₃²/(2λ₃) = E