  It will be shown that starting from a coordinate system where the 6 phase
space coordinates are linearly coupled, one can go to a new coordinate system
where the motion is uncoupled by means of a linear transformation. The original
coupled coordinates and the new uncoupled coordinates are related by a 6x6
matrix, R. R will be called the decoupling matrix. It will be shown that of the
36 elements of the 6x6 decoupling matrix R, only 12 elements are independent.
This may be contrasted with the results for motion in 4-dimensional phase
space, where R has 4 independent elements. A set of equations is given from
which the 12 elements of R can be computed from the one period transfer
matrix.This set of equations also allows the linear parameters for the
uncoupled coordinates to be computed from the one period transfer matrix. An
alternative procedure for computing the linear parameters and the 12
independent elements of the decoupling matrix R is also given which depends on
computing the eigenvectors of the one period transfer matrix. These results can
be used in a tracking program, where the one period transfer matrix can be
computed by multiplying the transfer matrices of all the elements in a period,
to compute the linear parameters and the elements of the decoupling matrix R.
