Analytical methods of calculation of powered and passive trajectory of reactive and rocket-assisted projectiles

Abstract

Context. Within the framework of the accepted simplifying hypotheses, an approximate scheme of calculation of the parameters of the active and passive sections of the trajectory is proposed, which allow to study the trajectory properties of the existing as well as perspective samples of the reactive and rocket assisted projectiles. The object of the study is a model for the calculation of the trajectories of the reactive and rocket assisted projectiles based on a nonlinear system of differential equations of motion of the center of mass of the solid. Purpose. The purpose of the work is to propose for practical apply a new system of corrections in the range and direction for deviation of the flight conditions of the projectiles from the table value, based on the calculations of elements of the trajectory of the projectiles at the end of the active section of the trajectory, which greatly improves the accuracy of preparation of installations for firing and as a result  the effectiveness of hitting the target. Objective. The goal of the work is to propose a new system of corrections in the range and direction for deviation of the flight conditions of the projectiles from the table value, based on the calculations of elements of the trajectory of the projectiles at the end of the active section of the trajectory, which greatly improves the accuracy of preparation of installations for firing and as a result  the effectiveness of hitting the target. Method. The proposed analytical method allows to: determine the set of indicators characterizing the process of approaching the rocket projectile from the guide and clarify the initial conditions necessary to solve the system of equations of motion on the active section of the trajectory; which is regarded as a standalone trajectory that affects the course of the projectile's flight on the active section of the trajectory. The calculation of the passive trajectory plot for rocket projectile and the second passive plot for active rockets projectile is necessary to obtain the trajectory parameters at the point of fall (in the vicinity of the target) which is important for the correction of fire in the subsequent defeat of the target by reactive (active-reactive) projectile's (mortar shells). Results. The developed calculation method was tested in the estimation of the accuracy of the calculation of the elements of the trajectory of projectile movement. Conclusions. The calculations performed on the basis of the developed analytical method confirm the workability of the proposed mathematical support and allow recommending it for practical use in solving problems of external ballistics with the prospect of optimizing the trajectory of motion of controlled and unmanaged flying objects. Prospects for further research are to create consistent methods for calculating tactical and technical indicators of new types of ammunition.