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Hi,

I want to estimate the rotation angles I need to apply to align the galactic plane of a given galaxy in TNG50 with the cartesian axes X,Y,Z. I'm using the tensor of inertia to align the galaxy, so the transformation I've made was

        I[0,0] = np.sum( masses * (xyz[:,1]*xyz[:,1] + xyz[:,2]*xyz[:,2]) )
        I[1,1] = np.sum( masses * (xyz[:,0]*xyz[:,0] + xyz[:,2]*xyz[:,2]) )
        I[2,2] = np.sum( masses * (xyz[:,0]*xyz[:,0] + xyz[:,1]*xyz[:,1]) )
        I[0,1] = -1 * np.sum( masses * (xyz[:,0]*xyz[:,1]) )
        I[0,2] = -1 * np.sum( masses * (xyz[:,0]*xyz[:,2]) )
        I[1,2] = -1 * np.sum( masses * (xyz[:,1]*xyz[:,2]) )
        I[1,0] = I[0,1]
        I[2,0] = I[0,2]
        I[2,1] = I[1,2]

        # get eigen values and normalized right eigenvectors
        eigen_values, rotation_matrix = np.linalg.eig(I)

        # sort ascending the eigen values
        sort_inds = np.argsort(eigen_values)
        eigen_values = eigen_values[sort_inds]

        # permute the eigenvectors into this order, which is the rotation matrix which orients the
        # principal axes to the cartesian x,y,z axes, such that if axes=[0,1] we have face-on
        new_matrix = np.matrix( (rotation_matrix[:,sort_inds[0]],
                                 rotation_matrix[:,sort_inds[1]],
                                 rotation_matrix[:,sort_inds[2]]) )

        new_matrix = new_matrix*np.matrix( ((0,1,0),(0,0,1),(1,0,0)) )

with new_matrix, the rotation matrix. Once I have the galaxy aligned, I want to recover the Euler angles theta,Psi,phi from the previous rotation to convert from the initially randomly oriented galaxy to the edge-on/face-on one. I assume the rotation matrix with the triad of angles is given by

and of course, as theta can adopt 2 different values, I will have two values of phi and psi as well, however, when I'm trying to recover the initial rotation matrix with the angles I've obtained, the values I get are not even similar. It is the Euler matrix of the image not correct? Is there any easiest way to get the Euler angles?

Thanks in advance,
Pablo

Assuming it is a normal rotation matrix, these instructions should work?

I've solved the problem. One of the angles was rotated by a factor pi/2.

Thanks