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.