Explicit "ballistic M-model": A refinement of the implicit "modified point mass trajectory model"

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.