09. Movement of a corpuscle in the air in conditions of wind and movement of the unit

Smaglij V. I.
Pages: 56-60.

Full article: 
Abstract
The purpose. To develop high-precision procedure of approximate integration of equations of movement of material corpuscle launched into the air in condi­tions of wind and movement of the unit. Methods. Approximation is used in equations of members V N-1V , V N-1V yandV N-1V Z by polynomials of 3rd, 4th and so on etc. degree in the time t. The first values of quotients of these polynomials are calculated using the equations of zero approximation which are brought in the article. The subsequent values can be gained by iteration, i.e. integration of the equations with these polynomials with their fixed clarification by averaging previous val­ues and values which were received after integration of Vx, Vy, and Vz, up to their coincidence. Results. The de­veloped multiple-purpose procedure enables to receive practically any accuracy of calculation of parameters of movement of a corpuscle on the taken segment of its movement in conditions of wind and movement of the unit. Conclusions. This procedure is simple enough, can compete to procedure of calculation executed by means of numerical methods, can be applied in determination of accuracy of such calculations and in integration of other equations which are not integrated in elementary functions.

Key words: equation, zero approximation, approxi­mation, methods of iteration, averaging, clarification, comparison, coincidence.

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