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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 6/spl times/6 matrix, R. It will be shown that of the 36 elements of the 6/spl times/6 decoupling matrix R, only 12 elements are independent. 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, the /spl beta//sub i/, /spl alpha//sub i/, i=1, 3, for the uncoupled coordinates, to be computed from the one period transfer matrix.

The Linear Parameters and the Decoupling Matrix for Linearly Coupled Motion in 6 Dimensional Phase Space