a j axis pivot and its lower end hookes joint attachment as an i axis pivot consequently the rotation of each rod relative to its predecessor is compound first there is rotation of the hookes joint intermember 33 relative to the upper rod 30b around the i axis then the lower rod 30a is rotated relative to the hookes joint intermember 33 by some amount around the new j axis thus the lower rod is rotated relative to its predecessor rod by an i axis body rotation followed by a j axis body rotation the machined ends and the hookes joint connectors preserve the 90 u00b0 relationship between the pivot axes at the two ends of the rod therefore the rotation matrix m by which the lead rod is rotated relative to the rod behind it i e relative to its own previous position at the last preceding update is described by equ1 where u03b1 i axis angle of rotation the rotation m updates the attitude matrix m of the lead rod in the preceding lead rod attitude where a b c are readings of accelerometers 21 22 23 then by definition of the solution set we require those which give small values of u03b1 and u03b2 i e cos u03b1 and cos u03b2 as large as possible these are equ2 these solutions are then combined to form m and the end rod.