Handling Rotational Degrees of Freedom in Coordinate Transformations

[chinmay]

I am trying to analyse response of a dynamic system. The source disturbance is about x,y,theta (rotation about x ) & Phi of one coordinate system (red coloured coordinate system in the attached figure).

I need to get the response in another coordinate system ( green coloured coordinate system in the attached figure), whose all three axis is inclined to initial coordinate system.

In case of only x & y,it can be easily done using transformation matrix, but how to handle the transformation of rotational dof.

I tried to convert the source disturbance in spherical coordinate system , then cartesian, then transformation and finally again to (X, Y, Z, THETA, PHI, PSI,) new coordinate system; but this process is to tedious.

Is there any better alternative is available ?

 

[FactChecker]

There is probably no easier way. If some of the transformations are constant, they can probably be combined into a consolidated transformation matrix. When using phi, psi, theta Euler angles, you need to be careful about "gimbol lock", where the angles are not well defined and it is hard to represent motion continuously. That can force you to use quaternions, which is a can of worms. Hopefully, you will not need to use quaternions.