A parallel RLC circuit, with source.

We can use the established rules to write the Lagrangian function for the circuit as: . We also use Kirchhoff's current law to impose a constraint function of Ψ  =  i_R + i_L + i_C − i_S  =  0, and we use the principle of the Lagrange multiplier to obtain an ordinary differential equation to describe the dynamical behaviour of v(t).