# R2xyz: Find the three rotation angles about new axes in the xyz... In nvctr: The n-vector Approach to Geographical Position Calculations using an Ellipsoidal Model of Earth

## Description

The angles (called Euler angles or Tait–Bryan angles) are defined by the following procedure of successive rotations: Given two arbitrary coordinate frames A and B, consider a temporary frame T that initially coincides with A. In order to make T align with B, we first rotate T an angle x about its x-axis (common axis for both A and T). Secondly, T is rotated an angle y about the NEW y-axis of T. Finally, T is rotated an angle z about its NEWEST z-axis. The final orientation of T now coincides with the orientation of B. The signs of the angles are given by the directions of the axes and the right hand rule.

## Usage

 `1` ```R2xyz(R_AB) ```

## Arguments

 `R_AB` a 3x3 rotation matrix (direction cosine matrix) such that the relation between a vector v decomposed in A and B is given by: v_A = R_AB * v_B

## References

Kenneth Gade A Nonsingular Horizontal Position Representation. The Journal of Navigation, Volume 63, Issue 03, pp 395-417, July 2010.

`xyz2R`, `R2zyx` and `zyx2R`.
 ```1 2 3 4 5 6``` ``` R_AB <- matrix( c( 0.9980212 , 0.05230407, -0.0348995 , -0.05293623, 0.99844556, -0.01744177, 0.03393297, 0.01925471, 0.99923861), nrow = 3, ncol = 3, byrow = TRUE) R2xyz(R_AB) ```