Intermediate-Axis Linear Stability
Compare stable and unstable rotations through the eigenvalues of a rigid body’s linearized Euler equations.
Free theory articleCompare stable and unstable rotations through the eigenvalues of a rigid body’s linearized Euler equations.
Concept & interpretation
The stability of a freely rotating rigid body depends on which principal axis it spins about. By linearizing Euler's equations of motion about a steady rotation, we can determine the nature of small perturbations.
Experiment
You can verify this calculation and visualize the perturbation trajectories in the Intermediate-Axis Linear Stability module.
- Set the Inertias to One two three.
- Set the Principal axis to 2 (the intermediate axis).
- Ensure the Spin rate is set to 1.
- Set the Time to 2.
- Leave the Perturbation at 0.001.
- Observe the exponentially diverging trajectory in the phase portrait canvas and the resulting numeric values.
- Change the Principal axis to 1 or 3 to observe closed, oscillatory orbits (oscillatory stability).