It can be shown that a stable bullet has to fulfil three different conditions:
Statically unstable handgun bullets will hardly be met in "real life", because such a projectile would be useless. However, when fired with insufficient spin, "well-designed" bullets may be statically unstable.
It is possible to define a static stability factor sg and derive a static (or gyroscopic) stability condition, which simply demands that this factor must exceed unity.
As an example, the figure displays the static stability factor for the 7.62 x 51 Nato M80 bullet, fired at 32° to the horizontal. The M80 bullet exits the muzzle with a static stability factor of 1.35. Obviously, the static stability factor continuously increases at least for the major part of the trajectory or more generally, always exceeds its value at the muzzle. Generally, it can be assumed that if a bullet is statically stable at the muzzle, it will be statically stable for the rest of its flight.
If, on the contrary, a bullet is dynamically unstable, the angle of yaw increases.
The occurrence of an initial yaw close to the muzzle is by no means an indicator of bullet instability. In some recent publications, the statements "bullet is unstable" and "bullet shows a (big) yaw angle" are used synonymously which is incorrect. On the contrary, an initial yaw angle at the muzzle is inevitable and results from various perturbations.
Bullets fired from handguns are not automatically dynamically stable. Bullets can be dynamically unstable at the moment they leave the barrel. Other bullets are dynamically stable close to the muzzle and loose dynamic stability as they continue to travel on, as the flowfield changes.
The figure schematically shows an over-stabilized bullet fired at a high angle of elevation, which lands base first.
Mathematically, a bullet is said to be tractable, if the tractability condition is fulfilled.