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Symmetry and conserved quantities for non-material volumes

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Abstract

This paper investigates the Lie symmetry and conserved quantities of non-material volumes. The Lie symmetrical determining equations of the system are presented by introducing the invariance of equations of motion for the system under general infinitesimal transformation of Lie groups. The structure equations and the form of conserved quantities are calculated. And three kinds of conserved quantities, i.e., Noether, Lutzky and Mei conserved quantities of the systems, are derived. In addition, the Hojman conserved quantity of the systems is proposed under the special infinitesimal transformations. An example is given to illustrate the application of the method and result, and four kinds of conserved quantities are obtained under the Lie symmetrical transformations.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 11702119, 51779109 and 11502071), the Natural Science Foundation of Jiangsu Province (Nos. BK20170565 and BK20171306) and the Innovation Foundation of Jiangsu University of Science and Technology (1012931609 and 1014801501-6).

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Authors and Affiliations

  1. Department of Engineering Mechanics, Jiangsu University of Science and Technology, Zhenjiang, 212003, China

    Wen-An Jiang

  2. College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124, China

    Li-Li Xia

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  1. Wen-An Jiang
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  2. Li-Li Xia
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Correspondence to Wen-An Jiang.

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Jiang, WA., Xia, LL. Symmetry and conserved quantities for non-material volumes. Acta Mech 229, 1773–1781 (2018). https://doi.org/10.1007/s00707-017-2076-0

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