The theory of linear damped oscillations was originally developed more than hundred years ago
and is still of vital research interest to engineers mathematicians and physicists alike. This
theory plays a central role in explaining the stability of mechanical structures in civil
engineering but it also has applications in other fields such as electrical network systems
and quantum mechanics. This volume gives an introduction to linear finite dimensional damped
systems as they are viewed by an applied mathematician. After a short overview of the physical
principles leading to the linear system model a largely self-contained mathematical theory for
this model is presented. This includes the geometry of the underlying indefinite metric space
spectral theory of J-symmetric matrices and the associated quadratic eigenvalue problem.
Particular attention is paid to the sensitivity issues which influence numerical computations.
Finally several recent research developments are included e.g. Lyapunov stability and the
perturbation of the time evolution.
