Abstract：The Noether symmetry and conserved quantity of the second-order Lagrange system on time scales are studied in this paper. The equations corresponding to the second-order Lagrange system on time scales are introduced. Then based on the principle of invariance of Hamilton interaction under infinite small group transformation， the generalized Noether symmetric transformation of the second-order Lagrange system and the definition and criteria under the generalized Noether quasi-symmetric transformation are studied. The Noether theorems under the general infinitesimal transformation are obtained. An example is given to illustrate the application of the theorem.
2021, Vol. 55 
