Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

If a rigid body, rotating freely in 3d, experiences no friction or other external forces and has an initially diagonal inertia matrix $\mathbf{I}_0$ (with $I_{11}>I_{22}>I_{33}>0$) and initial angular velocity $\omega_0$ relative to an external inertial reference frame, it seems that the orientation and angular velocity as a function of time must be deterministic from the initial conditions.

I believe that conservation of angular momentum tells us:

$\tau = \frac{dL}{dt} = \mathbf{R}_t\mathbf{I}_0\mathbf{R}^\text{T}_t\dot{\omega}_t+\omega_t \times \mathbf{R}_t\mathbf{I}_0\mathbf{R}^\text{T}_t\omega_t$

Computing this iteratively is possible, but not very accurate. Explicit integration tends to gain energy like crazy. Is there a known, closed-form solution for $\mathbf{R}_t$ and $\omega_t$ as a function of time, assuming that $\mathbf{R}_0$ is the identity matrix?

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.