A generalization of Noether's theorem for a non-material volume

作者：Casetta Leonardo^*; Irschik Hans; Pesce Celso Pupo

来源：ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 2016, 96(6): 696-706.

DOI：10.1002/zamm.201400196

• Non-material volumes
• Ritz's method
• generalized Noether's theorem
• conservation laws
• rotating drum uncoiling a strip

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]. 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]. 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.

• 出版日期2016-6