Optimization of One-Dimensional Sectional Systems

The optimum design of sectional systems is conducted with an equal-strength rod considered for illustration. Conditions are found for sectioning the non-uniform rod of a designed mass in such a way that the total length of the rod should be maximal. Relative masses of the series sections are shown to follow the golden section rule for uniform constructions. A function is suggested for evaluating the difference between parameters of an-section rod, optimized for the maximum length, and a model of the equal-strength continuous construction. Conditions are defined for optimum relations between sequential modes of one-stage rocket engines with different flow rates, given the maximum velocity at the end of an active leg of the rocket vertical flight in the gravitational field.