Differential equations can be transformed into algebraic equations by using an integration property of the orthogonal functions and the so-called operational matrix of integration. In this way, the calculation effort performed by the identification process or sensitivity analysis of mechanical systems can be reduced. For this purpose, mechanical systems are represented by state-space equations and the input and output signals are developed in series of orthogonal functions. After the integration of these equations a simple set of algebraic equations is obtained, which leads to the determination of the unknown parameters, such as modal and structural parameters, excitation forces, initial conditions and sensitivity functions. Different orthogonal functions were tested in numerical and experimental applications, including gyroscopic systems.
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