Acta Mechanica

, Volume 229, Issue 4, pp 1773–1781 | Cite as

Symmetry and conserved quantities for non-material volumes

  • Wen-An JiangEmail author
  • Li-Li Xia
Original Paper


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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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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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Engineering MechanicsJiangsu University of Science and TechnologyZhenjiangChina
  2. 2.College of Mechanical EngineeringBeijing University of TechnologyBeijingChina

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