Calculus Model for a Rolling Guided Missile

Abstract

The paper presents the relations that form the basis for the calculus models needed to study rolling guided missiles. The equations of the general motion are written within the Resal trihedral in a way that allows, after linearization, one to draw up a structural scheme of the controlled object, a scheme that will be used in the guided missile system analysis. Opposite to the flying machines with stabilized roll where the analysis is done after decoupling the channels, for the missile with rotation, the analysis of the scheme is done simultaneously on both channels, as terms used are complex terms. Furthermore, there will be presented some characteristics of this type of missile by analyzing a model close to the one of an antichariot missile with gasodynamic control.The basic notations are according to standards presented by Ni~a et al.

Stability of Single Channel Homing Slow-Rolling Missile

“…The problem of rotationally guided missiles has been addressed in several stages and forms in the literature. Some of these works refer to two-channel rotation missiles [5][6][7], and others to singlechannel missiles with time-modulated control [8][9][10][11]. Among the two-channel rockets, there is a Disclaimer/Publisher's Note: The statements, opinions, and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s).…”

“…Another category of papers aims to define sensors with which to determine the attitude, especially the roll angle of the rocket necessary to form the command signal [17,18]. Since we intend to address the case of the timecontrolled single-channel missile, we will analyze in detail the results obtained in papers [8][9][10][11].…”

“…In paper [10], starting from the equations of motion written in the Resal frame, a linear model of the command motion for the slow-rotating rocket is constructed. Due to the coupling between channels given by gyroscopic and Magnus terms, the linear model is constructed with complex coefficients, highlighting both nutation and precession motion and defining the flying quality parameters in complex form.…”

“…The linear development of the commanded motion ends with constructing a structural scheme of the commanded object specific to the slow-rolling missile with complex coefficients. Unlike work [9], which uses serial development, in work [10], the generation of the switch command for a single-channel missile is done considering the sign of a trigonometric expression dependent on the roll angle, as shown in [19]. Further in the paper [10] are analyzed two models of slow-rolling single-channel guided missiles, the portable anti-aircraft single-channel homing missile and the portable anti-tank single-channel wire-guided missile.…”

“…Unlike work [9], which uses serial development, in work [10], the generation of the switch command for a single-channel missile is done considering the sign of a trigonometric expression dependent on the roll angle, as shown in [19]. Further in the paper [10] are analyzed two models of slow-rolling single-channel guided missiles, the portable anti-aircraft single-channel homing missile and the portable anti-tank single-channel wire-guided missile. Unlike work [9], which forms the command in the body frame, in work [10], starting from the duration modulated form of the command, an equivalent command is obtained in the Resal frame with which, in the end, structural diagrams of the guided missile are built for the two cases: homing missile and a wireguided missile.…”