The role of virtual work in Levi‐Civita's parallel transport | Zendy

Iurato Giuseppe | Zendy; Ruta Giuseppe | Zendy

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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) - holonomic , covariant derivative , interpretation (philosophy) , virtual work , computation , work (physics) , simple (philosophy) , curvature , parallel transport , christoffel symbols , manifold (fluid mechanics) , covariant transformation , gravitation , holonomic constraints , classical mechanics , differential (mechanical device) , calculus (dental) , physics , mathematics , computer science , mathematical analysis , mathematical physics , geometry , engineering , algorithm , epistemology , mechanical engineering , philosophy , finite element method , artificial intelligence , 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)

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