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I'm visualising the motion of a rigidbody in 3D space with MATLAB and Simulink using this library which implements 6DOF equations of motion based on applied forces and moments.

Here is my model so far on Simulink. I have the outputs of the block being saved into the MATLAB workspace to run in a visualization software i've written. enter image description here

I am confused though on the difference between the Euler angles and the angular position. In the picture above, I've integrated the angular rates to get the angular positions. Comparing the display to the Euler angle display I get different sets of angles. Below is what my visualization looks like: enter image description here

Should I be visualizing the orientation of the block with the Euler angles or the angular position (integrated angular rates) i.e. which values are the true angles of the rigidbody in the body frame?

I think the answer I'm looking for is in the docs I linked above (pic below) however I'm still not understanding the difference between [phidot thetadot psidot] and [p q r]. Additionally I want to s

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    $\begingroup$ 1 Are you familiar with 3-axis gimbal systems? 2 The 3 components of the body rates resolved in the body frame are not supposed to be integrated independently (that is what the simulink 1/s block does). You have to transform $(p,q,r) \rightarrow (\dot{\theta}, \dot{\psi}, \dot{\phi})$ using the matrix formula (which you have put in the question) and integrate those to arrive at $(\theta, \psi, \phi)$. $\endgroup$
    – AJN
    May 8, 2022 at 16:46

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I am confused though on the difference between the Euler angles and the angular position. In the picture above, I've integrated the angular rates to get the angular positions.

The angular position that is being referred seems to be the three components of the body rate integrated independently. The integrated result is not physically meaningful.

To get a physically meaningful result, the components cannot be integrated independently. The formula involving Euler angles (there are other techniques also) is given in the question itself

equation from the question inserted here for completeness

I'm still not understanding the difference between $\dot \phi, \dot \theta, \dot \psi$ and $p, q, r$.

(p, q, r) is a vector whose direction indicates the instantaneous axis of rotation of the body. Its magnitude represents the angular rate about that axis.

To visualise $\dot \phi, \dot \theta, \dot \psi$, one can use the concept of Gimbal mechanisms. They show the rate of rotation of the 3 individual rotation linkages in the gimbal mechanism. Animation from Wikipedia

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