LAUSR

This paper is concerned with adiabatic invariants, applied to Noether symmetrical perturbation of disturbed non-material volumes. The disturbed equation of non-material volumes is proposed, the identity of Noether symmetry for the disturbed system is described, and the corresponding Noether exact invariant is derived. The perturbation to the Noether symmetry and adiabatic invariant for non-material volumes is employed by introducing the concept of adiabatic invariant. The Noether identity of symmetrical perturbation for the disturbed non-material volumes is reported, and Noether adiabatic invariant is obtained. Two examples are given to illustrate the application of the method, and the corresponding exact invariant and adiabatic invariant are obtained under the Noether symmetrical transformations.