A Modal Analysis for the Damped Linear Gyroscopic Systems

A modal analysis of a flexible linear damped gyroscopic system is developed here. The simple structure of the corresponding real constant generally nonsymmetric dynamic matrix allows the use of the biorthogonality relation and dual-expansion theorem for a linear operator in a vector space. A closed-form response to both periodic forces and general initial conditions is thus obtained. The method is illustrated by deriving the response of an inertially coupled gravity-stabilized pervasively damped satellite.