Algorithms for coordinate transformations

Overview

For convenience we divide the algorithms into several groups as follows:

• transformations between different geocentric systems,
• transformation to local horizontal coordinates,
• transformations between different heliocentric systems,
• minimum variance analysis to determine a transformation to boundary normal systems,

Background information

There are a number of common issues which one must consider when performing coordinate transformations:

• Time systems. Most coordinate transformations are time-dependent. We provide a description of the time systems used on these pages.
• Use of matrix methods. Vector and tensor quantities in space physics may be conveniently transformed between different coordinate systems using matrix arithmetic as introduced by Russell (1971) and extended by Hapgood (1992). We provide a description of the matrix formalism used on these pages.
• Spherical form. We provide a description of the methods to convert vectors between cartesian (x, y, z) and spherical (range, latitude, longitude) forms.
• Rotation angles. We provide a description of the various rotation angles which must be calculated before building the transformation matrices.

Last updated 16 July 1997 by Mike Hapgood (Email: M.Hapgood@rl.ac.uk)