AIDJEX Bulletin #40 - Polar Science Center - University of Washington

The equations governing solutions along stress and velocity characteristics
(75) and (79) can now be written explicitly in terms of the components
u, u, OI and y. However, as we determine the specific form taken by each
characteristic equation, the use of a subscript ci = 1, ..., 4 becomes cumbersome.
Therefore, it is helpful to introduce another notational scheme to be
used to express final results in term of components. In the new notation,
eigenvalues associated with stress characteristics are defined by
The orientation angles associated with these roots are IC+
-
where
tan K+ =
-
Ot
and the coordinates along each stress characteristic curve are
A similar set is introduced to define velocity characteristics. Characteris-
tic roots are
?J, = A3
4
The associated angles v,
-
satisfy
tan v, =
-
1-1,
(84)
and the coordinates along each velocity characteristic curve are
The use of the symbol f is especially useful because roots and equations
along either stress or velocity characteristics differ only in a few signs,
If we return to the governing equation along stress characteristics