# Change in angle due to rotation

1. Jun 28, 2011

### Laiva-59

Hi,

I have the following problem:

A rigid body, to which an axis system xyz is attached, has an orientation defined by Euler angles phi, theta and psi with respect to an intertial frame XYZ.

The Euler angles are defined as explained on wikipedia and can be thought of as a rotation matrix as shown in following link:
http://en.wikipedia.org/wiki/Rotati...)#Conversion_formulae_between_representations

Now, on this fixed body, I would like to find (on a given point), the angle the outer surface normal makes with the XY-plane. I found the outer surface normal in the body-fixed coordinates N = [nx, ny, nz].

Q's:

1. How now to find the angle with plane XY (Z=0)? (call it beta)
2. If we rotate the body along phi,theta and psi, how does this beta change?

So basically: If we have defined this angle, how does the angle change when we rotate the axes?