Ballistic flight of a projectile with two precessional modes

Rapidly spinning projectiles with infinite rotational symmetry display a high degree of physical correspondence to a classical gyroscope. As with a gyroscope, such projectiles show two precessional modes, one of which will always be in evidence during a flight. Aeroballistic theory provides, additionally, for two simultaneously excited nutational modes, with sinusoidal frequencies close to, but not exactly coincident with, the precessional angular velocities. The combination of these two orthonormal rotations gives rise to complex pitching and yawing motion, which can be substantially different than the motion predicted by aeroballistic theory alone. Results from a numerical integration of the equations of motion in their most general form illustrate these differences.