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.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.