Abstract: The author studied the Noether symmetries and conserved quantities of non-conservative singular systems in phase space on time scales. Firstly, the internal constraints caused by singularity were treated as external non-holonomic constraints, and the canonical equations of constrained Hamiltonian systems were obtained by using Hamilton principle under Δ derivative on time scale. Secondly, the special infinitesimal transformation with time invariance was introduced, and the criterion and theorem of Noether symmetry were obtained according to the invariance of Hamilton action. Finally, the effectiveness of the method and results was
 illustrated by an example. The results show that the structural properties of canonical equations of constrained Hamiltonian systems on time scale are still maintained, the singularity of the system makes the Noether symmetry no longer directly lead to the Noether-type conserved quantity, and it is necessary to construct a certain gauge function to make the Noether symmetry satisfy the structural equation.

Key words: time scale, constrained Hamiltonian system, Noether symmetry, conserved quantity