Modularity and Causality in Physical System Modelling

Abstract

Decomposition and reassembly of a physical system should not change the form of its describing equations; the physics and mechanics describing each component of a machine remain the same whether the components are separate or assembled into a complete system. In general, the differential equations used to model physical systems do not share this property. This paper considers restrictions on the structure of mathematical models of physical systems which endow the equations with the same modularity as the physical system. It is shown that models based on nonenergic junctions (ideal series and parallel connections) cannot guarantee this property. Generalized energic junction structures are proposed and it is shown that they are sufficient to guarantee modularity.