Hojman conserved quantities of discrete mechanico-electrical systems constructed by continuous symmetries

Hojman conserved quantities and Lie symmetries of mechanico-electrical coupling systems are studied. Firstly, choosing a new structure equation which is different from Hojman's form, Hojman's theorems, Hojman conserved quantities and Lie symmetries of continuous mechanico-electrical coupling systems are studied. Secondly, based upon the property of the discrete models entirely inheriting the symmetry of the continuous systems, Hojman conserved quantities and Lie systems of discrete mechanico-electrical coupling systems are presented by Lie groups of transformations of continuous systems; the determining equations of invariance of difference equations and the difference grid are obtained for discrete mechanico-electrical systems; the discrete analogue of Hojman conserved quantities of mechanico-electrical systems are constructed by associated continuous invariant models. Finally an example is discussed to illustrate the results.