Mathematical models of many systems in engineering, theoretical physics and other domains in natural sciences have the character of a differential system defined on a certain net, which consists of one-dimensional elements arithmetized in local length coordinates. These elements (recti- or curvi-linear) are interconnected at nodes, through which energy and mass are streaming being functions of time. The system as a whole is fixed through boundary conditions or interconnected with other sub-systems. Elements of the system are considered with continuously distributed parameters (mass, stiffness, conductivity, etc.). External energy is supplied by means of boundary conditions or by element and node excitation. The problem of a system response or a relevant eigen-value problem can be understood as a problem of a differential system on an orientated graph. This graph is a corresponding geometric representation of the mechanical system investigated, where elements of the graph are individual bars of the system. As an illustration of this theoretical study the conventional slope deflection method developed in the past for statics and later for dynamics of continuous frames is outlined. Some more illustrations from other disciplines are also given. The character of the resulting algorithm is close to the finite element method if special macro-elements provided by the direct solution of relevant differential system are used.

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