The elastica can be understood from a number of different aspects, including as a mechanical equilibrium, a problem of the calculus of variations, and the solution to elliptic integrals.
In particular, we propose a formal solution to a puzzle composed of non-trivial objects (such as holes and strings) assuming a version of the Situation Calculus written over first-order Equilibrium Logic, whose models generalise the stable model semantics.
Local analysis makes use of differential calculus, and stability analysis of equilibrium points.
In this work, we extend the SIR model with vaccination to a fractional-order model and give a detailed analysis of the equilibrium points of the model by applying fractional calculus.
By applying fractional calculus, we give a detailed analysis of the equilibrium points of the model.
In particular, general equilibrium theorists used general topology, convex geometry, and optimization theory more than differential calculus, because the approach of differential calculus had failed to establish the existence of an equilibrium.
The virtual displacement principle and calculus of variation techniques are implemented to obtain the equilibrium equations.
By adopting procedures that were becoming familiar in analytical mechanics and following from the principle of virtual work as introduced in 1717 by Johann Bernoulli for such discrete systems as pin-connected rigid bodies, Euler rendered the energy stationary and in this way developed the calculus of variations as an approach to the equations of equilibrium and motion of elastic structures.
Moreover, differential calculus has returned to the highest levels of mathematical economics, general equilibrium theory (GET), as practiced by the "GET-set" (the humorous designation due to Jacques H. Drèze).
Governing equations derived either from using calculus of variations or from statics correspond to errors in satisfying in-plane equilibrium equations and/or constitutive relations.
