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A generalization of Noether's theorem for a non‐material volume
Author(s) -
Casetta Leonardo,
Irschik Hans,
Pesce Celso Pupo
Publication year - 2016
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201400196
Subject(s) - noether's theorem , mathematics , generalization , control volume , conservation law , calculus (dental) , variety (cybernetics) , context (archaeology) , invariant (physics) , solid mechanics , mathematical analysis , lagrangian , physics , mechanics , medicine , paleontology , statistics , dentistry , mathematical physics , biology , thermodynamics
Variable‐mass conditions can occur in a variety of practical problems of engineering. Investigations on problems of this type have been figuring as a particular research field of mechanics and applied mathematics. The fundamental issue is that the basic equations of classical mechanics were originally formulated for the case of an invariant mass contained in a material volume. Therefore, appropriate formulations are required when dealing with variable‐mass problems. The scope of the present article is devoted to arbitrarily moving control volumes formulated within the framework of Ritz's method, that is, to non‐material volumes in the sense discussed by Irschik and Holl [10][H. Irschik, 2002]. We aim at demonstrating a generalized version of Noether's theorem such that it can be grounded on the generalized Hamilton's principle for a non‐material volume in the form derived by Casetta and Pesce [17][L. Casetta, 2013]. This will consistently allow the consideration of conservation laws, written from a Noetherian approach, in this particular context of non‐material volumes. To test the proposed formulation, the problem of a rotating drum uncoiling a strip will be addressed.