A substantial proportion of all dynamic models arising naturally present th
emselves initially in the form of a system of second-order ordinary differe
ntial equations. Despite this, the established wisdom is that a system of f
irst-order equations should be used as a standard form in which to cast the
equations characterizing every dynamic system and that the set of complex
numbers, and its algebra, should be used in dynamic calculations, particula
rly in the frequency domain. For any dynamic model occurring naturally in s
econd-order form, it is proposed that it is both intuitively and computatio
nally sensible not to transform the model into state-space form. Instead, i
t is proposed that Clifford algebra, Cl-2, be used in the representation an
d manipulation of this system. The attractions of this algebra are indicate
d in three contexts: 1) the concept of similarity transformations for secon
d-order systems, 2) the solution for characteristic roots of self-adjoint s
ystems, and 3) a model reduction for finite element models.