Formalization of the Gateaux derivative of functional and application in the principle of virtual work

Abstract

Abstract Analytical mechanics provides the central guidelines for the design of engineering machinery in use today. One of the main pillars for analytical mechanics is the principle of virtual work. In the establishment of this principle, the Gateaux derivative plays an indispensable role. In this paper, we formalize the Gateaux derivative in the interactive theorem prover HOL Light. On this basis, we formally verify the principle of virtual work. This effort paves way for the computerized formalization of analytical mechanics. Thus, it will ultimately contribute to the verified design of engineering machinery, which comes with correctness guarantees beyond what is enabled by the currently adopted validation techniques.