d’Alembert’s principle

In mechanics, d’Alembert’s principle is a reformulated version of the second law of motion which gives an interpretation of the force of inertia, which allows one to extend the principle of virtual work from statics to dynamics, according to which one can extend the criteria of equilibrium—vanishing of a force in Newtonian mechanics means equilibrium—to a system which is in motion. [1]

History
The so-called d’Alembert’s principle was formulated by French mathematician physicist Jean D'Alembert.

This vanishing of forces in dynamical system principle is often called d'Alembert's principle, but, according to Arnold Sommerfeld (1956), it was first written in this variational form by Joseph Lagrange. [5]

Physical economics
The principle of d’Alembert, according to physical economics historian Philip Mirowski, is said to have been influential and or thematically found in the 1801 economic formulations of French mathematician and engineering Nicholas-Francois Canard. [3]

In 1897, French engineer and physical socioeconomist Vilfredo Pareto penned a mechanical-to-social phenomena variables table, in a section of which he made the following comparison: [4]

The science of mechanics is divided into two others. If we consider inextensibly connected material points we obtain a pure science, rational mechanics, which studies in an abstract way the forces of equilibrium and movement. The easiest part of science is equilibrium. D’Alembert’s principle, considering the forces of inertia, enables the reduction of the dynamic problem to a static one.The science of political economy is divided into two others. If we consider the homo economicus who acts only as a result of economic forces, we obtain political economy, which studies in abstract terms ophelimity. The only part of this which is well known is static equilibrium. There may be a principle for economic systems analogous to D’Alembert’s, but at present our knowledge is very poor. The theory of economic crisis offers an example of dynamic study.

References
1. Lanczos, Cornelius. (1949). The Variational Principles of Mechanics (§4: D’Alembert’s Principle, pgs. 88-). Dover, 1970.
3. Mirowski, Philip. (2004). The Effortless Economy of Science? (pg. 287). Publisher.
4. (a) Pareto, Vilfredo. (1896). Course of Political Economics (Cours d’Economie Politique), Volume One. University of Lausanne.
(b) Pareto, Vilfredo. (1897). Course of Political Economics (Cours d’Economie Politique), Volume Two (variables table, pgs. 12-13). University of Lausanne.
(c) Pareto, Vilfredo. (1964). Cours d’Economie Politique (variables table, pgs. 12-13). Librairie Droz.
(d) McLure, Michael. (2002). Pareto, Economics and Society: the Mechanical Analogy (molecules, pg. 124; molecule, 4+ pgs; comparison table, pg. 65-66). Routledge.
(e) Donzelli, Franco. (1997). “Pareto’s Mechanical Dream” (pdf) (comparison table, pgs.2-4), History of Economic Ideas, 3:127-78.
5. Arnold Sommerfeld (1956), Mechanics: Lectures on Theoretical Physics, Volume One (p. 53). Academic Press, 1964.

External links
D’Alembert’s principle – Wikipedia.
d’Alembert’s principle – Britannica.

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