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. 2014 Feb 28;9(2):e77190. doi: 10.1371/journal.pone.0077190

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© 2014 Allison et al

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

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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).

Inline graphic — 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).