ABSTRACT
Until this point we have assumed that the projectile has been an axially symmetric body. This allowed us to simplify the equations of motion considerably. Projectiles are rarely axially symmetric. The asymmetry usually comes about through manufacturing tolerances, damage due to rough handling, cargo slippage or, more recently, they are simply designed that way. The purpose of this section is simply to introduce the geometry of mass asymmetries, which will be introduced into the equations of motion for the projectile in later sections. Mass asymmetries come in two categories: static imbalance and dynamic imbalance. In a
static imbalance, the center of gravity (CG) of the projectile is not located on the geometric axis of symmetry. The geometric axis of symmetry can be defined by imagining a projectile with the same exterior dimensions as the unbalanced projectile but of uniform density. The symmetry axis would then be centrally located in the body of revolution (i.e., a perfectly axially symmetric body). In a statically imbalanced projectile, this axis would be shifted to pass through the CG but remain parallel to the geometric axis. This is illustrated in Figure 10.1. A dynamically imbalanced projectile also has a CG that is offset from the geometric axis
of symmetry. In this case, however, the mass distribution is such that the principal axis of inertia resides as some angle to the geometric axis as well. This is illustrated in Figure 10.2.
