DOI: https://doi.org/10.33099/2311-7249/2018-33-3-139-142

DETERMINATION OF ANALYTICAL DEPENDENCE FOR INITIAL RATIO OF FORCES WITH CONSIDERING OF CRITERIA LIMITATIONS

Ihor S. Romanchenko, Volodymyr P. Kotliarov, Oleksandr O. Pavliuk

Abstract


This article considers an approach which is based on the analysis of the system of differential equations of the medium dynamics method to determine the general analytical dependence of the ratio of forces with considering of criterion limitations.
Equations of medium dynamics are considered in the nonlinear formulation, when the coefficients of the effect depend on the number of statuses.
The article describes the approaches of the theory of differential equations to determine the general integral convolution (general integral of the system).
The criteria for achieving the objective of operation are the amount of affordable losses of the one of the sides and the required ratio of forces. Taking into account the criteria limitation, proposed approach allows to determine the required time for conducting an operation, as well as, if necessary, the initial amount of required number of forces of the one of sides for guaranteed achievement of the operations objective.
The solution of the system of differential equations allows us to calculate the reference graph (reference trajectory) of the ratio of forces coefficient changing in time, in accordance with conditions of the criteria limitations.


Keywords


military formations; ratio of forces; criterion limitation; differential equation

References


Romanchenko I.S., Kotliarov V.P., Shapoval Y.E. Numerical interpretation of the dynamics of the change in the ratio of forces of the sides during the combat actions // The collection of scientific works, The CRI of the AFU, Kyiv, 2008. # 4 (46) P. 11–15.

Kotliarov V.P., Pavliuk O.O., Blinov O.V., Kuznetsov O.A. Identification of the coefficients of the intensity of effect based on the results of numerical calculations. The collection of scientific works, The CRI of the AFU, Kyiv, 20016. # 3 (77) P. 33–38.

Bronshtain I.N., Semendiaev K.A. Mathematical Reference Book for Engineers and Students. Translation from German under editionGrosheI.and Zigler V. Leipzig: Toibner.Moscow: Nauka. The main editorial office of the physical and mathematical literature. 1981. 720 p.


GOST Style Citations


1. Романченко І. С. , Котляров В. П. , Шаповал Ю. Є. Чисельна інтерпретація динаміки змінення співвідношення сил сторін під час ведення ними бойових дій  // Зб. наук. пр. ЦНДІ ЗС України. Київ, 2008. № 4 (46). С. 11–15.

2. Котляров В. П., Павлюк О. О., Блінов О. В, Кузнєцов О. А. Ідентифікація  коефіцієнтів інтенсивності вражаючого впливу за результатами чисельних розрахунків  // Зб. наук. пр. ЦНДІ ЗС України. Київ, 2016. № 3 (77). С. 34–38.  

3. Бронштейн И. Н., Семендяев К. А. Справочник по математике для инженеров и учащихся втузов. Пер. с нем. под ред. Гроше Г. и Циглера В. Лейпциг: Тойбнер, Москва: Наука. Глав. ред. физ.-мат. лит-ры. 1981. 720 с.





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