On the general structure of mathematical models for physical systems

Abstract

It is proposed that the mathematical models for any physical systems that are based in first principles, such as conservation laws or balance principles, have some common elements, namely, a space of kinematical states, a space of dynamical states, a constitutive law that associates dynamical states with kinematical states, as well as a duality principle. The equations of motion or statics then come about from, on the one hand, specifying the integrability of the kinematical state, and on the other hand, specifying a statement that is dual to it for the dynamical states. Examples are given from various fundamental physical systems.

34 pages; Ann. Phys. (Berlin), 1-25 (2011)

References in corpus (5)

• On the Axioms of Topological Electromagnetism
• Groups of motions and mechanics I: point mechanics
• Integrability and the variational formulation of non-conservative mechanical systems
• A generalization of Noether's theorem based on the virtual work functional
• On the pre-metric foundations of wave mechanics I: massless waves