Approaches to finding the trade-off region on a monotonically decreasing asymmetric curve in cost-time coordinates

When designing a space mission, the problem of choosing between two mutually inverse quantities often arises, for example, between the ΔV costs and the flight duration, between the ΔV costs and the maneuver execution altitude. The same problem is encountered in analysis of already plotted Pareto-front. The peculiarity of such problems is that the function y(x) under study is monotonically decreasing; its derivatives are often monotonic as well. Planning a particular maneuver calls for choosing the so-called compromise point or region in the interval from “a to b”, after reaching which the decrease of the function y(x) does not bring a noticeable gain with further increase of the argument. Intuitively, the position of this trade-off region is well guessed, but when using automated decision support tools, more rigorous calculation methods are required. The paper considers approaches to finding a compromise point on the plot of a monotonically decreasing function close to the right branch of a hyperbola and asymmetric with respect to the right angle bisector. The vague definition of the trade-off makes one search for different methods based on understandable physical or geometric principles, but insensitive to units. The found solutions are tested for the case of coplanar and non-coplanar flight using the drift orbit. © 2025 Elsevier B.V., All rights reserved.