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The role of virtual work in Levi‐Civita's parallel transport
Author(s) -
Iurato Giuseppe,
Ruta Giuseppe
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510342
Subject(s) - interpretation (philosophy) , holonomic , covariant derivative , computation , work (physics) , simple (philosophy) , curvature , christoffel symbols , parallel transport , virtual work , manifold (fluid mechanics) , covariant transformation , gravitation , differential (mechanical device) , holonomic constraints , classical mechanics , calculus (dental) , physics , mathematics , computer science , mathematical analysis , mathematical physics , geometry , engineering , epistemology , algorithm , philosophy , mechanical engineering , artificial intelligence , finite element method , medicine , dentistry , thermodynamics , programming language
According to current history of science, Levi‐Civita introduced parallel transport solely to give a geometrical interpretation to the covariant derivative of absolute differential calculus. Levi‐Civita, however, searched a simple computation of the curvature of a Riemannian manifold, basing on notions of the Italian school of mathematical physics of his time: holonomic constraints, virtual displacements and work, which so have a remarkable, if not dominant, role in the origin of parallel transport. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)