0
$\begingroup$

Suppose we have an evolving system describing a rigid body by euler angles with respect to the bodies center. Suppose we do a constant offset parameter transformation for the euler angles, in other words suppose we re-define the center of the coordinate system with respect to a different set of euler angles. Does the body fixed frame angular velocity vector get changed during this process?

Since it's body fi xed frame I would like to say it does not get changed, can someone explain?

$\endgroup$

1 Answer 1

1
$\begingroup$

enter image description here

Two coordinate systems that not parallel to each other are attached to a rigid body

the transformation matrix between system "1" and inertial system is described by the three Euler angles

$$S_1=S_1[\alpha(t)~,\beta(t)~,\gamma(t)]$$

the transformation matrix between system "2" and inertial system is $$S_2=S_s^T\,S_1\,S_s$$

where $~S_s$ is a static transformation that make at $t=0$ the two coordinates system parallel to each other , you can describe the static coordinate system also by a three Euler angles they are time independent .

the angular velocity $~\vec\omega=[\omega_x'~,\omega_y'~,\omega_z']~$ can obtained from this equation

$$\begin{bmatrix} 0 & -\omega_z' & \omega_y' \\ \omega_z' & 0 & -\omega_x' \\ -\omega_y' & 0 & \omega_x' \\ \end{bmatrix}=S_2^T\,\dot{S_2}$$

where the components of the angular velocity $~\vec \omega~$ are given in body fixed coordinate system "2".

$\endgroup$
2
  • $\begingroup$ So do you just apply the transformation to the angular velocity vector? $\endgroup$ Jun 5, 2021 at 19:30
  • $\begingroup$ yes , this is how you obtain the angular velocity matrix with the transmission matrix and the time derivative of the transformation matrix. $\endgroup$
    – Eli
    Jun 5, 2021 at 20:43

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.