Comparison of two modified point-mass trajectory models of an artillery shell

Abstract

The modified point-mass trajectory model of an artillery shell, proposed by R. Lieske and M. Reiter, determines the trajectory with the high accuracy and requires tens of times less computational resources than the rigid body trajectory model. This modified model is based on an approximate implicit formula for the dynamic equilibrium position of the symmetry axis of the shell, obtained by the authors under some physically motivated assumptions. In the present article, the motion of a fast spinning artillery shell as a rigid body is described by an ODE system, where expressions of aerodynamic forces and moments are taken, which are linearized in the total angle of attack. It is established that the definition of the dynamic equilibrium position of the symmetry axis of the shell, proposed by R. Lieske and M. Reiter, differs from its definition as a quasi-stationary solution of the equations of angular motion of the symmetry axis only by the lack of the pitch damping moment coefficient. By small parameter methods, an error estimate is obtained for the trajectory, describing by the modified point-mass trajectory model, in comparison with the trajectory, describing by the linearized ODE system with the same initial data for the variables of translational motion and axial rotation.