Radiation Induced Instability

In this paper we discuss the stability and instability properties of two classes of conservative dynamical systems which are comprised of a finite dimensional and an infinite-dimensional sub-system. The finite dimensional component is a linear mechanical system with gyroscopic terms and it is coupled to a wave equation defined on an infinite spatial domain via two different types of coupling-integral and point coupling. In addition to the wave equation we also consider coupling to the Klein-Gordon equation. In particular here we analyze the conditions under which connection to a wave system induces instability in the finite dimensional system. Analytic results are compared to simulations.