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# Transformation between Terrestrial Frames

Fundamentals | |
---|---|

Title | Transformation between Terrestrial Frames |

Author(s) | J. Sanz Subirana, J.M. Juan Zornoza and M. Hernández-Pajares, Technical University of Catalonia, Spain. |

Level | Intermediate |

Year of Publication | 2011 |

From elemental linear algebra, all transformations between two Cartesian coordinate systems can be decomposed in a shift vector , three consecutive rotations around the coordinate axes (, , ), and a scale factor (). That is, they can be described by the following equation, which involves 7 parameters:

where:

Adopting the convention used by IERS, the previous equation (1) can be written as follows:

where , , are three translation parameters, is a scale factor and , and are three rotation angles.

Transformation parameters from ITRF2000 to past ITRFs are listed in table 4.1 of IERS Conventions (2003) [Denis et al., 2004].^{[1]}

## References

- ^ [Denis et al., 2004] Denis, D., McCarthy and Petit, G., 2004. IERS Conventions (2003). IERS Technical Note 32. IERS Convention Center., Frankfurt am Main.