Noether symmetry and conserved quantities of electromechanical systems on time scales

Abstract

This paper investigates Noether symmetry and its associated conserved quantities in electromechanical systems formulated on time scales. First, based on the Lagrange–Maxwell equations for electromechanical systems, a general description of holonomic systems is established in terms of generalized coordinates. Subsequently, by applying the Hamilton principle on time scales, the Lagrange–Maxwell equations for electromechanical systems are derived within the time-scale framework. On this basis, a theorem concerning the Noether conserved quantities for such systems is proposed and rigorously proved. Furthermore, the corresponding Noether conservation corollaries are obtained for both continuous-time and discrete-time cases. These results provide a unified theoretical framework that encompasses the conservation laws for the two classes of systems. Finally, the effectiveness and applicability of the proposed theory are validated through a practical case study involving an electromagnetic piston.