I have a system determined by 3 Euler angles that describe the orientation with respect to a fixed coordinate system XYZ.

The angular velocities are: $\omega_2$ (precession), $\omega_1$ (nutation) and $\omega_z$ (spin). The angular acceleration of $\omega_z$ is $\alpha_z$. The other angular accelerations are 0.

How can I find the acceleration of a point (e.g. A on the spinning reference frame xyz)? I am looking for the procedure to follow.

enter image description here


1 Answer 1


First of all you need to be about which reference frame you are estimating the acceleration of A. I assume you need the accelation of A wrt to the inertial frame of reference.

The most generic way is to link the acceleration of A to B. Then find the acceleration of B with respect to O.

See the following link for a starting point

The bottom line is that if you need the acceleration of P with respect to O, then you'll probably just need the following two equations:

$$\vec{v}_P =\vec{v}_O + \vec{\omega}\times \vec{r}_P$$ $$\vec{a}_P =\vec{a}_O + \dot{\vec{\omega}}\times \vec{r}_P + \vec{\omega}\times \left( \vec{\omega}\times \vec{r}_P\right)$$

  • $\begingroup$ I need it indeed wrt the initial reference frame. This was the confirmation. I needed. Thanks. $\endgroup$ Aug 11, 2020 at 20:47

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.