Minimal problems in airplane performance

We develop here the theory of operating an airplane so as to minimize an arbitrary function of the end-values of the generalized coordinates. A propeller-driven airplane is treated as a particle in equilibrium, subject to the forces of drag, lift, thrust, and gravity. We assume that the specific fuel consumption is a function of the power only, and that the available power is independent of the altitude. The problem is shown to be of the Bolza type in the Calculus of Variations, with the complications arising from the presence of inequalities, discontinuities, and variables whose derivatives do not enter the problem explicitly. The Euler-Lagrange equations are derived and discussed.