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We study the explicitly time-dependent response of a razor-thin axisymmetricdisc to externally imposed perturbations by recasting the linearizedCollisionless Boltzmann equation as an integral equation and applying Kalnajs'matrix method. As an application we consider the idealized problem ofcalculating the dynamical friction torque on a steadily rotating,two-dimensional bar. We consider two choices of basis functions in the matrixmethod, showing that both lead to comparable results. The torques from ourlinearised calculation are in excellent agreement with those measured from$N$-body simulation, as long as the bar perturbation does not resonate with asignificant fraction of the disc's stars.

On the self-consistent time-dependent linearized response of stellar discs to external perturbations