The role of virtual work in Levi-Civita's parallel transport |
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| Authors: | Giuseppe Iurato Giuseppe Ruta |
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| Institution: | 1. Department of Physics and Chemistry, University of Palermo, Italy;2. Department of Structural and Geotechnical Engineering, University “La Sapienza”, Rome, Italy |
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| Abstract: | 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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