Abstract
In this paper, a new kind of symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e. a Noether–Lie symmetry, is presented, and the criterion of this symmetry is also given. The Noether conserved quantity and the generalized Hojman conserved quantity of the Noether–Lie symmetry of the system are obtained. The Noether–Lie symmetry contains the Noether symmetry and the Lie symmetry, and has more generalized significance.
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