# Homework Help: Euler angles

1. Apr 4, 2008

### bman!!

First: the earth rotates with angular frequency w, with the rotation vector in the z direction. it is then useful to define a local coordinate system i', j', k' fixed on the earths surface (i.e. a cartesian coordinate system for us in our point of view on the surface of the earth) then to perform calculations it is easy enough to simply take components of w in the local coordinate system.

so components of w in local coordinates are (0,wsinx, wcosx) where x is the colatitude angle (at the north pole x = 0, and at equator x= 90)

having established this:

when using euler angles (im looking at yzy convention or simply y convention) are the angles still interpreted as referenced to the original i,j,k coordinate system?, so that in problems when you express k in components of e1' and e2' (the new axes after rotation) is this similar conceptually to the above situation?