Principal component analysis of flexible systems--Open-loop case

A generic class of flexible systems, characterized by finitely many lightly damped harmonic oscillators, is analyzed by means of the "open-loop principal component analysis," that is, singular value analysis and Gramian balancing. As the main result, it is shown that, as the damping ratio goes to zero, the balanced state coordinates are decoupled and coincide with the modal coordinates. Further, simple formulas expressing the "asymptotic singular values" as functions of the modal parameters are derived.