The approximate calculation methods of the extra-atmospheric active trajectory leg

Space technologies


Karagodin V. V.

Institute of Strategic Stability of State Corporation Rosatom, 9, Luganskaya St., Mosсow, 115304, Russia



Object of the research is the approximate and numerical methods for flight vehicles trajectories calculation, used in ballistics design during cycle development, and estimations of their basic design-ballistic characteristics.
Article theme is comparison of solution methods to the motion differential equations at the extra-atmospheric site of a trajectory in accuracy, main parameters, algorithmic and program methods of speed calculations increasing.
The activity purpose is working out and selection of the most effective methods of motion differential equations solution by "accuracy-speed" criterion, allowing to reduce volume and time of calculations with the decreasing of calculation accuracy level of trajectory kinematics parameters in design-ballistic problems.
The accuracy characteristics of the known and new methods of the motion equations solution are received with the help of numerical calculation computer methods with their corresponding increasing of process and calculation time.
In this article it is shown that for motion problem at the extra-atmospheric active trajectory leg the known approximate numerical methods of the motion equations integration are more effective in accuracy in comparison with others. The analytical solution to linear motion equations is received. Numerical methods which can be used for the approximate of solution to the motion equations with large step of integration are resulted. Algorithmic methods of calculation speed increasing are offered. Semianalytical formulas are developed for derivative calculation of motion parameters according to factors of the pitch program.
Results of activity can find application in the field of ballistics design and selection of the basic design-ballistic parameters of flight vehicles. For the considered problem the most effective parameter "accuracy-speed" is the modified by Nuström’s method with semianalytical expressions for derivative calculation of trajectory kinematic parametres. The use of this method allows to reduce solution time of regional ballistic problem not less than in 2-3 times in comparison with other considered methods.


motion equations, the extra-atmospheric trajectory active leg, solution method, accuracy, response


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