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The matrices and defined in (2.80) can be found
analytically for circular crosssection using the standard integral in
equation (A.1) of appendix A.
A full derivation is given in appendix B.
The result is that each element is a
function of
and the element is given by

(2.85) 
where and and

(2.86) 
When the change in crosssection tends to zero (ie. tends to 1)
we obtain

(2.87) 
with being the identity matrix (a diagonal matrix with all the entries
having a value of 1). is the fractional change in crosssection,
and is a matrix whose
elements are given by

(2.88) 
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Jonathan Kemp
20030324