Abstract
Various models of a projectile in a resisting medium are used. Some are very simple, like the “point mass trajectory model”, others, like the “rigid body trajectory model”, are complex and hard to use, especially in Fire Control Systems due to the fact of numeric complexity and an excess of less important corrections. There exist intermediate ones - e.g. the “modified point mass trajectory model”, which unfortunately is given by an implicitly defined differential equation as Sec. 1 discusses. The main objective of this paper is to present a way to reformulate the model obtaining an easy to solve explicit system having a reasonable complexity yet not being parameter-overloaded. The final form of the M-model, after being carefully derived in Sec. 2, is presented in Subsec. 2.5.
References
[1] R.L. McCoy, Modern Exterior Ballistics. The Launch and Flight Dynamics of Symmetric Projectiles, Schiffer Publishing, Atglen, 1999.
[2] L. Baranowski, “Effect of the mathematical model and integration step on the accuracy of the results of computation of artillery projectile flight parameters”, Bull. Pol. Ac.: Tech. 61 (2), 475-484 (2013).
[3] L. Baranowski, “Equations of motion of spin-stabilized projectile for flight stability testing”, J. Theoretical and Applied Mechanics 51 (1), 235-246 (2013).
[4] L. Baranowski, “Numerical testing of flight stability of spin stabilized artillery projectiles”, J. Theor. Appl. Mech. 51 (2), 375-385 (2013).
[5] R.F. Lieske and M.L. Reiter, Equations of Motion for a Modified Point Mass Trajectory, Report No. 1314, U.S. Army Ballistic Research Laboratory, New York, 1966.
[6] L. Baranowski, “Feasibility analysis of the modified point mass trajectory model for the need of ground artillery fire control systems”, J. Theoretical and Applied Mechanics 51 (3), 511-522 (2013).
[7] B. Zygmunt, K. Motyl, B. Machowski, M. Makowski, E. Olejniczak, and T. Rasztabiga, “Theoretical and experimental research of supersonic missile ballistics”, Bull. Pol. Ac.: Tech. 63 (1), 229-233 (2015).
[8] R. Głębocki, “Guidance impulse algorithms for air bomb control”, Bull. Pol. Ac.: Tech. 60 (4), 825-833 (2012).
[9] G. Kowaleczko and A. Żyluk, “Influence of atmospheric turbulence on bomb release”, J. Theor. Appl. Mech. 47 (1), 69-90 (2009).
[10] Z. Dziopa, I. Krzysztofik, and Z. Koruba, “An analysis of the dynamics of a launcher-missile on a moveable base”, Bull. Pol. Ac.: Tech. 58 (4), 645-650 (2010).
[11] Z. Koruba and E. Ładyżyńska-Kozdraś, “The dynamic model of a combat target homing system of an unmanned aerial vehicle”, J. Theor. Appl. Mech. 48 (3), 551-566 (2010).
