Abstract
Based on the invariance of Birkhoffian equations under the infinitesimal transformations of groups, the definition and the criterion of a form invariance for a Birkhoffian system are established. The condition under which the form invariance can lead to a non-Noether conserved quantity and the form of the conserved quantity are deduced by relying on the total time derivative along the trajectory of the equations and two corollaries in special cases are presented. An example is finally given to illustrate the application of the results.
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