Normal isoperimetric extremal
= Normal isoperimetric extremal
{title2=$\delta J=\lambda\,\delta I$}
A constrained <extremal> is normal when the constraint <functional> has a nonzero <first variation> in some allowed direction. The <implicit function theorem> then permits a compensating variation, yielding a multiplier equation with objective coefficient normalized to one. The <Euler-Lagrange equation> applies to the objective integrand minus the multiplier times the constraint integrand.