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

Transversal: International Journal for the Historiography of Science 2:166 (2017)
  Copy   BIBTEX

Abstract

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 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. 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.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 76,419

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

The role of virtual work in Levi-Civita’s parallel transport.Giuseppe Iurato & Giuseppe Ruta - 2015 - Proceedings of Applied Mathematics and Mechanics 15:705-706.
Mathematics Ab Ovo: Hans Driesch and "Entwicklungsmechanik".Silvia Waisse-Priven & Ana M. Alfonso-Goldfarb - 2009 - History and Philosophy of the Life Sciences 31 (1):35 - 54.
Mechanics in Six-Dimensional Spacetime.V. S. Barashenkov - 1998 - Foundations of Physics 28 (3):471-484.
Metaphysics of the principle of least action.Vladislav Terekhovich - 2018 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 62:189-201.
The Unifying Laws of Classical Mechanics.C. D. Bailey - 2002 - Foundations of Physics 32 (1):159-176.
Random dynamics and the research programme of classical mechanics.Michal Tempczyk - 1991 - International Studies in the Philosophy of Science 5 (3):227 – 239.

Analytics

Added to PP
2017-12-16

Downloads
16 (#670,075)

6 months
2 (#300,644)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Raffaele Pisano
Université des Sciences et Technologies de Lille

References found in this work

Physics.Daniel W. Aristotle & Graham - 2018 - Hackett Publishing Company.
De Caelo. Aristotle - 2020 - Hackett Publishing Company.
Mècanique Analytique (Analytical Mechanics).J. L. Lagrange - forthcoming - Boston Studies in the Philosophy of Science.

View all 26 references / Add more references