Equations of Projectile Motion in a Flexible Gun Tube

This interim report presents the formulation of a system of simultaneous differential equations which describes the general motion of a projectile of finite geometry and inertia traveling in a flexible gun tube. The formulation permits the projectile six degrees-of-freedom relative to the gun tube; three orthogonal translational motions of the projectile c.g. relative to the instantaneous gun tube axis and three (Eulerian) rotational motions of the projectile about it c.g. The formulation is presented in terms of interior ballistics data, projectile design data, and gun tube design and motion data. The formulation accounts for projectile spin, mass eccentricity, elastic deformation of the projectile rotating band and bourrelet, and projectile/bore interfacial friction and torque transmission. Furhtermore, the formulation is unrestricted regarding the nature of gun tube motion. The formulation has been compared with projectile descriptions and formulations employed by other investigators and, based upon this comparison, isconsidered to be the most generally applicable projectile in-bore motion formulation appearing in recent literature.