Abstract:The Noether symmetries of constrained Birkhoffian systems on time scales were studied. Based on the principle of PfaffBirkhoff on time scales, the Birkhoff′s equations with multipliers on time scales for a constrained Birkhoffian system were established. The Noether identity on time scales was given, and the Noether symmetry of the constrained Birkhoffian system on time scales was defined. The Noether′s theorem of the constrained Birkhoffian system on time scales was proposed and proved, which revealed the relationship between the Noether symmetry and conserved quantity. Two special cases of the Noether′s theorem were given for a free Birkhoffian system on time scales and a classical constrained Birkhoffian system. Finally, a numerical example was presented to illustrate the effectiveness of this method.