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

CHARACTERISTIC EQUATIONS
The ordinary differential equations that must be satisfied along each
real characteristic direction have been discussed formally in an earlier section
(eqs. 31-39). In this section we look at several special cases that
help us to understand the general result, and we discuss the complete set of
equations e
Eigenvectors 2-
-a
of equation (33) must be found for each characteristic
direction A These vectors can then be used in equation (38) to derive the
a'
gcverning characteristic equations. If we divide the coefficient matrix
E) into appropriate 2x2 matrices (40). then it is desirable also to
4-
divide the eigenvectors similarly, To this end, let
R =
-a
S
a = 1, 2, 3 , 4
where i7
-a
&?,(Aa 4 - @>
-
and Sa are each two
and express the
the eigenvectors satisfy the
component vectors. If we form the product
result in terms of the submatrices, we find that
relationships (for each a)
m
m
After finding R and S from this linear algebraic set of equations, we
-a -a! m
substitute into the expression Q' A_, whichmay be rewritten as
-a
where
Ai2 Y =
i
b' sin 2y 2b cos 2y
(2 sin 2y B' - COS 21,
B' + cos 21,
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