Application of the Lambert function in the analytical solution of ballistics problems for flat flight trajectories of a material body, taking into account the gaseous (air) medium

Annotation. The paper describes the use of a special Lambert function for solving problems of ballistics of a material body, when the resistance of a gaseous (air) medium is taken into account. A model of quadratic (based on the speed of movement of a body) resistance of the medium within the limits of an approaching flat trajectory is considered. Problem. Problems of ballistics of a material body are considered in courses of theoretical mechanics, as well as in specialized literature. But, in addition to the cited literature, this research, like, for unraveling the simplified level of the material body in the problems of ballistics for flat trajectories of the power of a special function Lambert, which allows us to essentially simplify the algorithm for developing the parameters of the trajectory of a gentle slope (floor) type. Goal. The goal of the work is based on a framed model of a material body for flat trajectories in problems of modern ballistics on this basis, using a special Lambert function, to be controlled by a visible decoupling Didion, the determination of the main parameters of these types of crash trajectories. Methodology. Physic, mechanical and mathematical models are constructed that adequately describe the parameters of the collapse of a material body/particle that collapses along a flat trajectory when the wind is not supported , which are proportional to the square of the fluidity of the particles. For a more manual description of the parameters of the trajectory of the motion, there is a special Lambert function, which is tabulated in [1], or can be expanded with the help of computer in the middle of “Maple 8”. Practical value. The results obtained in the work can be used to improve and clarify engineering methods of calculation in problems of external ballistics of a material body, taking into account the quadratic (in terms of movement speed) resistance of the air environment