Preston, S. (2009) Noncommuting variations in the Lagrangian field theory and the dissipation. Il nuovo cimento C, 32 (1). pp. 159-172. ISSN 1826-9885
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Abstract
In this work we study the geometrical structure underlying the notion of noncommuting variations of dynamical variables in the Lagrangian field theory. We introduce the class of (twisted) prolongations of variations of dynamical fields to their derivatives that includes, as the special examples, the constructions of T. Levi-Civita, U. Amaldi, B. Vyjanovich and T. Atanaskovic and, finally, those of H. Kleinert and his coauthors. Usage of this variations procedure allows one to obtain non-potential forces terms in the corresponding Euler-Lagrange equations and the source terms in the energy-momentum balance laws. Obstructions for conservation of the brackets of vector fields of variations under twisted prolongation are found. As a special class of such twisted prolongations we introduce those defined by the connections on the bundles of vertical vector fields of the configurational bundle. As an application of this procedure, we get the entropy balance in the 4-dim geometrical model of material aging as the Euler-Lagrange equation for thermacy (thermical displacement) and show that it coincides with the entropy equation obtained for the Lagrangian written in the proper material space-time coordinates, using conventional flow prolongation of variations of dynamical fields.
| Item Type: | Article |
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| Uncontrolled Keywords: | Calculus of variations ; Global analysis and analysis on manifolds |
| Subjects: | 500 Scienze naturali e Matematica > 510 Matematica |
| Depositing User: | Marina Spanti |
| Date Deposited: | 24 Mar 2020 16:29 |
| Last Modified: | 24 Mar 2020 16:29 |
| URI: | http://eprints.bice.rm.cnr.it/id/eprint/16467 |
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