Title :

A Development of the Principle of Virtual Laws and its Conceptual Framework in Mechanics as Fundamental Relationship between Physics and Mathematics

Author(s) :

Pisano, Raffaele [Auteur correspondant]
Physique - IEMN [PHYSIQUE - IEMN]
Faculté des sciences de Lille
Université de Lille

Journal title :

Transversal: International Journal for the Historiography of Science

Pages :

166-203

Publisher :

Graduate Program in History of Federal University of Minas Gerais

Publication date :

2017-06-28

ISSN :

2526-2270

English keyword(s) :

Virtual laws
gravitas secundum situm
Relationships between Physics and Mathematics
Foundations of Physics

HAL domain(s) :

Physique [physics]/Physique [physics]/Histoire de la Physique [physics.hist-ph]
Mathématiques [math]/Mathématiques générales [math.GM]
Mathématiques [math]/Histoire et perspectives sur les mathématiques [math.HO]
Mathématiques [math]/Physique mathématique [math-ph]
Physique [physics]/Physique [physics]/Physique Classique [physics.class-ph]
Physique [physics]/Physique [physics]/Physique Générale [physics.gen-ph]
Sciences de l'Homme et Société/Histoire, Philosophie et Sociologie des sciences

English abstract : [en]

Generally speaking, virtual displacement or work concerns to a timely idea according to which a motion of a certain body is not the unique possible motion. The process of reducing this motion to a particular magnitude and ...
Show more >Generally speaking, virtual displacement or work concerns to a timely idea according to which a motion of a certain body is not the unique possible motion. The process of reducing this motion to a particular magnitude and concept, eventually minimizing as a hypothesis, can be traced back to the Aristotelian school. In the history and philosophy of science one finds various enunciations of the Principle of Virtual Laws and its virtual displacement or work applications, i.e., from Aristotle to Leibniz’s vis viva, from Maupertuis’ least action to Euler and Lagrange with calculus of variations (statics and dynamics) to Lazare Carnot’s mechanics. In this case study, I will demonstrate that a particular approach used by Lazare Carnot is original by explaining within the historical context of rival approaches such as the development of the Principle of virtual Laws (also known as the Principle of virtual velocity or of virtual work). I will also discuss Carnot’s geometric motion as one of the possible but invertible movements applied to virtual displacement as employed in his theories of machines and collisions. I will then go on to explore how the originality of an invertible motion within his mechanical and, in general, mathematical research program permitted Carnot to introduce a new way of structuring a scientific theory and making mechanics, with respect to the Newtonian paradigm, to scholars and his students of the École polytechnique de Paris.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Institut d'Électronique, de Microélectronique et de Nanotechnologie (IEMN) - UMR 8520

Source :

Harvested from HAL