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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