Coordinate Transformation in Rotational System Equations (Spacecraft Dynamics Block)

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Hi All;
The governing rotational system dynamic equatons page (link here) gives the following equation.
If you play around with the actual block, you will see that the moment of inertia matrix in this equation is given with respect to body fixed axis. The equation above however is written in inertial (i.e. ICRF) frame. So for example if you want to input the initial w_icrf2b, I believe the components are accepted in ICRF coordinate system. If this is the case, during the implementation of above equation, either we need to convert Mb and w_icrf2b vectors to body coordinate (like for example quatrotate(q_icrf2b, w_icrf2b)) and then implement the equation; OR first transform the inertia matrix to inertial frame (first find the transformation matrix between ICRF and body using q_icrf2b then I_icrf = R' * I_body * R where R is the transformation matrix) then implement the above equation by replacing I_mom = I_icrf.
If the above equation is implemented in the block by assuming that Mb and w_icrf2b are defined in inertial but already expressed in body frame, (which is the only explanation I have right now) then my discussion is no longer valid.
Is there anyone who can speculate about this topic ?
Many thanks

回答(1 个)

Paul
Paul 2024-11-9,1:33
Hi Gökhan,
Why do you think that the equation is written in inertial (i.e. ICRF) frame. It looks to me like that equation is the standard* form with all quantities written with respect to and resolved in the body-fixed coordinate frame.
*However, the equation as written is incorrect. The inv(Imom) that post-multiplies the right hand side should pre-multiply the right hand side. Hopefully that's just a mistake in the documentation and not the actual block implementation, which appears to be inaccessible to the user.
  1 个评论
Gokhan
Gokhan 2024-11-14,8:16
Hi @Paul;
Many thanks for your prompt response. the reason for my confusion is, because in the documentation of MATLAB there are little bits and pieces of discrepancies (like the one you mentioned), quite often a matrix is multiplied with a vector, from time to time the resolution frame is specified, at other times it is just implied etc. Also in the block there are a few other things that confused me. Thank you for your answer.

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