Vehicle's angular velocity w -> Rate of change of Euler angles

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Nick - 29 Feb 2008 01:57 GMT

I am sorry if this topic has been discussed but I didn't find much help
from the archive.

Some textbook said that there is a transformation matrix between:

Vehicle's angular velocity, note as [p q r]'
and
Rate of change of Euler angles, note as [phi_dot theta_dot psi_dot]'
(where the Euler angles are defined in inertial frame's orientation,
[phi theta psi]')

The transformation is:

[p q r]' = R [phi_dot theta_dot psi_dot]';

/ 1 0 -sin(theta) \
R = | 0 cos(phi) sin(phi)cos(theta) |
\ 0 -sin(phi) cos(phi)cos(theta)/

Some text derives the R from:
[p q r]' = i_3*phi_dot + j_2*theta_dot + k_1*psi_dot;

Home come there is such a R?? Thanks!~

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Androcles - 29 Feb 2008 02:52 GMT

|I am sorry if this topic has been discussed but I didn't find much help
| from the archive.
[quoted text clipped - 19 lines]
|
| Home come there is such a R?? Thanks!~

http://mathworld.wolfram.com/RotationMatrix.html

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Nick - 29 Feb 2008 03:11 GMT

Thanks, would you specify more?

> |I am sorry if this topic has been discussed but I didn't find much help
> | from the archive.
[quoted text clipped - 21 lines]
>
> http://mathworld.wolfram.com/RotationMatrix.html

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Androcles - 29 Feb 2008 04:00 GMT

| Thanks, would you specify more?

Not sure what you are asking. A 3x3 rotation matrix will transform
a set of points from one coordinate frame to another, the overall
effect is this:
http://www.androcles01.pwp.blueyonder.co.uk/B747.gif
http://www.androcles01.pwp.blueyonder.co.uk/Differential.gif

All that is really happening is the colour of a fixed position pixel is
changing.
An angular velocity is simply a new angle at a later time
just as a linear velocity is a new position at a later time.
Where you get "inertial" from only you would know.
The advantage of using one matrix is that it simplifies computation.

Are you asking how to combine 2D rotation matrices into a 3D
matrix? Maybe this is what you want:
http://mathworld.wolfram.com/EulerAngles.html

I'm not clairvoyant or telepathic, sorry. You'll need to say
what it is you want to know.

| > |I am sorry if this topic has been discussed but I didn't find much help
| > | from the archive.
[quoted text clipped - 21 lines]
| >
| > http://mathworld.wolfram.com/RotationMatrix.html

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Natural Science Forum / Physics / General Physics / February 2008

Vehicle's angular velocity w -> Rate of change of Euler angles