this coupling, use can be made of the primal or dual assembly method. Both assembly methods make use of the dynamic equations as was defined before: In these equations is again used to define the set of interface forces, which are yet unknown. Primal assembly In order to obtain the primal system of equations, a unique set of coordinates is defined: . By definition of an appropriate Boolean localisation matrix , a unique set of DoFs remains for which the compatibility condition is satisfied a priori (compatibility condition). In order to satisfy the equilibrium condition a second equation is added to the equations of motion: Pre-multiplying the first equation with yields the notation of the assembled equations of motion for the generalised coordinates : This result can be rewritten in admittance form as: This last result gives access to the generalised responses as a result of the generalised applied forces , namely by inverting the primally assembled impedance matrix. The primal assembly procedure is mainly of interest when one has access to the dynamics in impedance form, e.g. from finite element modelling. When one only has access to the dynamics in admittance notation, the dual formulation is a more suitable approach. Dual assembly A dually assembled system starts with the system written in the admittance notation. For a dually assembled system the force equilibrium condition is satisfied a priori by substituting Lagrange multipliers for the interface forces: . The compatibility condition is enforced by adding an additional equation: Substituting the first line in the second and solving for gives: The term represents the incompatibility caused by the uncoupled responses of the substructures to the applied forces . By multiplying the incompatibility with the combined interface stiffness, i.e. , the forces that keep the substructures together are determined. The coupled response is obtained by substituting the calculated back into the original equation: This coupling method is referred to as the Lagrange-multiplier frequency-based substructuring (LM-FBS) method. The LM-FBS method allows for quick and easy assembling of an arbitrary number of substructures in a systematic fashion. Note that the result is theoretically the same as was obtained above by application of primal assembly. Decoupling in the frequency domain In addition to coupling of substructures, one is also able to decouple substructures from assemblies. Using the plus sign as a substructure coupling operator, the coupling procedure could simply be described as AB = A