Noether symmetry and Lie symmetry of discrete holonomic systems with dependent coordinates

The Noether symmetry, the Lie symmetry and the conserved quantity ofdiscrete holonomic systems with dependent coordinates areinvestigated in this paper. The Noether symmetry provides a discreteNoether identity and a conserved quantity of the system. Theinvariance of discrete motion equations under infinitesimaltransformation groups is defined as the Lie symmetry, and thecondition of obtaining the Noether conserved quantity from the Liesymmetry is also presented. An example is discussed to show theapplications of the results.