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The Transformation of Linear SecondOrder ODEs into Independent SecondOrder Equations: Scientific Computing and Matrix Computations SeminarSeminar: Departmental  January 23  12:101 p.m.  380 Soda Hall Matthias Morzfeld, LBL Electrical Engineering and Computer Sciences (EECS) The class of linear secondorder dynamical systems is considered. These systems of coupled ordinary differential equations (ODE) are characterized by three symmetric positive definite (SPD) coefficient matrices: one arises from inertial terms, the second from Hooke's law, and the third from velocityproportional energy dissipation. The goal is to transform the coupled set of n secondorder ODEs into n independent (scalar) secondorder equations. In the absence of damping, this goal can be achieved by congruence transformation because two SPD matrices can be simultaneously diagonalized. However, three SPD matrices can not be simultaneously diagonalized by congruence transformations unless certain restrictive conditions apply, so in this case we must consider more general transformations. I will present a method that utilizes a real, invertible but nonlinear mapping to transform any set of coupled secondorder linear ODEs into independent equations. Two examples from earthquake engineering are provided to indicate the utility of this approach. odedsc@cs.berkeley.edu, 5105164321 

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