  We discuss the propagation of surface waves in an isotropic half space
modelled with the linear Cosserat theory of isotropic elastic materials. To
this aim we use a method based on the algebraic analysis of the surface
impedance matrix and on the algebraic Riccati equation, and which is
independent of the common Stroh formalism. Due to this method, a new algorithm
which determines the amplitudes and the wave speed in the theory of isotropic
elastic Cosserat materials is described. Moreover, the method allows to prove
the existence and uniqueness of a subsonic solution of the secular equation, a
problem which remains unsolved in almost all generalised linear theories of
elastic materials. Since the results are suitable to be used for numerical
implementations, we propose two numerical algorithms which are viable for any
elastic material. Explicit numerical calculations are made for alumunium-epoxy
in the context of the Cosserat model. Since the novel form of the secular
equation for isotropic elastic material has not been explicitly derived
elsewhere, we establish it in this paper, too.
