Isoperimetric constraint (${\int }_a^{b}G(t,y,y^{\prime })dt=C$)

An isoperimetric constraint fixes the value of an integral while optimizing another integral over functions. A constant Lagrange multiplier incorporates the constraint into the variational integrand, and the resulting Euler-Lagrange equation must be supplemented by the appropriate natural boundary conditions for a free endpoint. The name includes integral constraints more general than prescribed geometric length.