We continue to use the example introduced in
§2.1 and
Figure 2.1.
We again consider the case with arbitrary masses ,
and zero damping constants
. This simplifies the equations
of motion to
.
As in §2.3.8 we solve the equations of motion
by substituting
, where
is a constant vector
and
is a constant scalar to be determined. This leads
to
. Letting
, where
the Cholesky factor
,
we see that we need to compute the eigenvalues of the symmetric tridiagonal
matrix
shown in equation (2.2).
Now we note that the stiffness matrix can be factored as
,
where
and
Bidiagonal matrices have particularly fast and efficient SVD algorithms.