0
$\begingroup$

Are these terms used interchangeably to mean the same things?

I'm aware of the conversion between body rates (often, $[p, q, r])$ and Euler rates (commonly, [$\dot\phi, \dot\theta, \dot\psi])$. This answer suggests that Euler rates are inertial angular rates. As written in this answer, it would appear that 'body-frame angle rate' is the same as 'body-frame angular velocity'. I expected angular velocity (as a 3-vector, $\vec\omega =[\omega_1, \omega_2, \omega_3]$) to be a different quantity -- referring to wiki for 3D angular velocity.

Is angular velocity (expressed in body frame) the same as angle rate-of-change (expressed in the same body frame)?

$\endgroup$

1 Answer 1

1
$\begingroup$

In the industry, the elements of the angular velocity vector are called body rates, that is, each element of $\vec{\omega}=[p,q,r]$ is called roll rate, pitch rate and yaw rate.

However, they are decidedly not mathematical rates from the perspective that they are derivatives of some quantities. Unless it's a single axis rotation, you can't straight-up integrate the angular velocity in the hopes of getting something meaningful.

I've had an academic professor telling me a mouthful for calling angular velocity "body rates", but alas, that's the industry norm.

$\endgroup$
4
  • $\begingroup$ Thanks for this perspective -- this has confused me for a while! Could you clarify if these quantities are numerically the same? That is, if I know the reported angular velocity, $\vec\omega$, of a body, do its three elements really correspond to the rate of change of the three angles? Or is this generally too implementation/sensor specific? $\endgroup$
    – WesT
    Apr 19 at 7:53
  • $\begingroup$ academicflight.com/articles/aircraft-attitude-and-euler-angles $\endgroup$
    – Jim
    Apr 19 at 11:17
  • $\begingroup$ @WesT No, they do not! That's the whole point! The angular velocity is different than the rates of the attitudes. $\endgroup$
    – JZYL
    Apr 19 at 13:12
  • $\begingroup$ @JZYL I know; sorry, I should've phrased it differently: I wanted to know if the vector $[p, q, r]$ (body rates reported from a gyro, say) is indeed the angular velocity vector; that is, it numerically obeys the definition of angular velocity (have a direction perpendicular to the plane of rotation and a magnitude corresponding to the speed of rotation). I think I glean from your answer that it does. $\endgroup$
    – WesT
    Apr 19 at 17:33

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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