
The dynamic stability condition
Abbreviations
c_{D}

Drag
coefficient 
c_{La}

Lift
coefficient derivative 
c_{Mpa}

Magnus
moment coefficient derivative 
c_{mq}+c_{ma}

Pitch
damping moment derivative 
s_{g}

Gyroscopic
(static) stability factor 
s_{d}

Dynamic
stability factor 
Explanation
A projectile is said to be dynamically stable, if its yawing motion
of nutation and precession is damped out with time, which means that an
angle of yaw induced at the muzzle (the initial yaw) decreases.
A dynamic stability factor s_{d} can be defined from
the linearized theory of gyroscopes (assuming only a small angle of yaw)
and the above dynamic stability condition can be formulated. An
alternate formulation of this condition
leads to the illustrative stability triangle.
s_{d} however depends on five aerodynamic coefficients.
Because these coefficients are hard to determine, it can become very complicated
to calculate the dynamic stability factor, which varies as a function of
the momentary bullet velocity.
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