Clifford Algebraic Perspective on Linear Second-Order Systems
SD Garvey (Aston University), MI Friswell (University of Wales Swansea) & JET Penny (Aston University)
AIAA Journal of Guidance, Control, and Dynamics, Vol. 24, No. 1, January-February 2001, pp. 35-45
A substantial proportion of all dynamic models arising naturally present themselves initially in the form of a system of second-order ordinary differential equations. Despite this, the established wisdom is that a system of first-order equations should be used as a standard form in which to cast the equations characterising every dynamic system and that the set of complex numbers, and its algebra, should be used in dynamic calculations - particularly in the frequency domain. This paper proposes that for any dynamic model occurring naturally in second order form, it is both intuitively and computationally sensible not to transform the model into state-space form. It proposes instead that the Clifford Algebra, Cl2, be used in the representation and manipulation of this system. The attractions of this algebra are indicated in three contexts: 1) the concept of similarity transformations for second-order systems, 2) the solution for characteristic roots of self-adjoint systems and 3) model-reduction for finite element models.
This material has been published in the AIAA Journal of Guidance, Control, and Dynamics, Vol. 24, No. 1, January-February 2001, pp. 35-45. Unfortunately the copyright agreement with AIAA does not allow for the PDF file of the paper to be available on this website. However the paper is available from AIAA - see the link below.
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