Gyroscope

Explore a symmetric gyroscope (equal transverse moments I, axial I₃) with optional gravity torque from a center-of-mass offset along the axle.

• Body-frame Euler equations with spin about principal axis z.
• Gravity torque: τ = r × (mg) in the body frame.
• Steady precession (large spin): Ω ≈ mgr / (I₃ ω sin θ), θ = tilt from vertical.
• Torque-free motion shows nutation when ω is not along a principal axis.

Use a low time scale for slow motion. Drag the 3D view to orbit the camera.