Linear Theory of a Dual-Spin Projectile in Atmospheric Flight

Abstract

The equations of motion for a dual-spin projectile in atmospheric flight are developed and subsequently utilized to solve for angle of attack and swerving dynamics. A combination hydrodynamic and roller bearing couples forward and aft body roll motions. Using a modified projectile linear theory developed for this configuration, it is shown that the dynamic stability factor, SD), and the gyroscopic stability factor, SG, are altered compared to a similar rigid projectile, due to new epicyclic fast and slow arm equations. Swerving dynamics including aerodynamic jump are studied using the linear theory. FrEuler roll angle of the forward body. SAEuler roll angle of the aft body. u, v, wTranslation velocity components of the composite center of mass resolved in the fixed plane reference frame. PFRoll axis component of the angular velocity vector of the forward body expressed in the fixed plane reference frame. PARoll axis component of the angular velocity vector of the aft body expressed in the fixed plane reference frame. q, rComponents of the angular velocity vector of both the forward and aft bodies expressed in the fixed plane reference frame. X,Y,ZTotal external force components on the composite body expressed in the fixed plane reference frame. LF ,MF ,NFExternal moment components on the forward body expressed in the fixed plane reference frame. LAMANAExternal moment components on the aft body expressed in the fixed plane reference frame. TFTransformation matrix from the fixed plane reference frame to the forward body reference frame. TATransformation matrix from the fixed plane reference frame to the aft body reference frame.i., j., k Fixed plane unit vectors. CvViscous damping coefficient for hydrodynamic bearing.

Robust gain-scheduled autopilot design for spin-stabilized projectiles with a course-correction fuze

“…(72) and modulates them to compute the actuator controls, using the nose angular position through Eq. (8).…”

“…The 7-DoF nonlinear mathematical model for ballistic dual-spin projectiles [8] was extended for the guided case in [24] and is recalled here. The translational and attitude airframe dynamics, expressed in a non-rolling reference frame and projected on the body coordinate system (CS) B, are:…”

Predictive Control of a Munition Using Low-Speed Linear Theory

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Integrated pitch/yaw acceleration controller for projectile with rotating canards using linear quadratic control methodology

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