The approximate conserved quantity of the weakly nonholonomic mechanical-electrical system

We study the approximate conserved quantity of the weakly nonholonomic mechanical-electrical system. By means of the Lagrange—Maxwell equation, the Noether equality of the weakly nonholonomic mechanical-electrical system is obtained. The multiple powers-series expansion of the parameter of the generators of infinitesimal transformations and the gauge function is put into a generalized Noether identity. Using the Noether theorem, we obtain an approximate conserved quantity. An example is provided to prove the existence of the approximate conserved quantity.