Abstract
This Letter focuses on form invariance and Noether symmetries of mechanico-electrical systems. Based on the invariance of Hamiltonian actions for mechanico-electrical systems under the infinitesimal transformation of the coordinates, the electric quantities and the time, the authors present the Noether symmetry transformation, the Noether quasi-symmetry transformation, the generalized Noether quasi-symmetry transformation and the general Killing equations of Lagrange mechanico-electrical systems and Lagrange–Maxwell mechanico-electrical systems. Using the invariance of the differential equations, satisfied by physical quantities, such as Lagrangian, non-potential general forces, under the infinitesimal transformation, the authors propose the definition and criterions of the form invariance for mechanico-electrical systems. The Letter also demonstrates connection between the Noether symmetries and the form invariance of mechanico-electrical systems. An example is designed to illustrate these results.
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