State Equations of Electrical Networks from a Lagrangian Formulation

This correspondence presents a systematic method of obtaining the state equations for lumped linear bilateral electrical networks using energy-state functions and Lagrange's equation. By applying a specified set of holonomic constraint equations in addition to a Legendre transformation on a portion of the system energy-state function, modified Lagrangian and Rayleigh functions are formulated, which, when substituted into Lagrange's equation, yield equations of state with capacitor tree voltages and inductor link currents as state variables. An example is included to illustrate the procedure.