# Euler angles in latitude longitude space

Tags:
1. Jan 12, 2016

### meteo student

In most physics introductions Euler angles(pitch, roll, yaw) are defined with respect to Cartesian coordinate system.

If I chose not to use a Cartersian coordinate system but instead use a latitude, longitude and a proprietary vertical coordinate(and no back transformations to Cartersian coordinate system permitted) basis vector space how would the pitch, yaw, roll Euler angles be defined ?

What I mean by this is the following

Initially I have a point defined in terms of λ,∅ and the vertical coordinate is defined as ζ.

Now I rotate the axes (not the point !) to a new set of axes λ',∅',ξ'.

I want to be able to define the Euler angles with respect to these two sets of orthonormal vectors.

Last edited: Jan 13, 2016
2. Jan 14, 2016

### meteo student

I want to correct what I wrote yesterday. When a proprietary vertical coordinate is used there is no restriction of basis vectors being orthonormal. These are basically curvilinear coordinates in which the rotations are being performed.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook