Analytical determination of missile angle position taking into account the flexible oscillations

Аuthors

Komissarenko A. I.

Instrument Design Bureau named after academician A.G. Shipunov, 59, Shcheglovskaya Zaseka str., Tula, 300001, Russia

e-mail: kbkedr@tula.net

Abstract

Sometimes interaction of elastic transverse vibrations of the body with an incoming air flow is referred to as aeroelastic vibrations. The frequency of these vibrations typically is close to the body proper vibrations. The vibrations induce unwanted transverse inertial loads on the body, particularly when they reach high amplitudes.

In the case when the missile is represented as a perfectly solid bit or when it has a rigid body, only the small perturbations of the motion parameters are considered. It allows to obtain with regard to perturbations a linear system of differential equations with coefficients that depend on parameters of the unperturbed motion.

Small thrust vectors induced by transverse vibrations of the body with accurate within the second order of smallness result in no variations of the missile acceleration in longitudinal direction. This acceleration remains the same one as for the nonperturbed motion both in value and in direction. This is the reason why under the small perturbations the transverse motion can be considered regardless of the longitudinal motion. Within a short period of time the guided missile trajectory can be considered as a plain curve, which is little different from a straight line. Therefore, let us consider the nonperturbed motion of the missile within a short period of time as the straight-line motion.

The issues of influence of flexible oscillations on flying ballistic and strength characteristics are arising during the process of designing missiles with bigger lengthening. Flexible oscillations occur from the engine tractive force and aerodynamical forces.

In this article the missile is substituted for inhomogeneous pivot for the purpose of studying the flexible oscillations.

Consideration of missile as inhomogeneous pivot significantly simplifies the study of angle characteristics determination.

The differential equations of the missile motion with regard for flexible oscillation have been derived.

The differential equations of the missile motion include torque and forces of the generalized coordinates of transverse vibrations are first sounded.

In the presented work such characteristics as a tractive, ballistic, weight, aerodynamical and inertial one are substituted for average ones during missile operation.

First tone flexible oscillations are taken into account.

Analytical dependencies of slip angle change, speed vector change, missile longitudinal axis angle with regard for the flexible oscillations have been obtained.

Keywords:

flexible oscillations, first tone proper oscillations

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