Module precession_nutation 

Precession and Nutation Physics for Ballistic Projectiles

This module implements the complex angular motion of spinning projectiles:

• Precession: Slow coning motion of the projectile axis
• Nutation: Fast oscillatory motion superimposed on precession
• Angular momentum conservation
• Gyroscopic effects

Structs

AngularState

Complete angular state of the projectile

PrecessionNutationParams

Parameters for precession and nutation calculations

Functions

calculate_combined_angular_motion

Calculate the combined precession and nutation motion

calculate_epicyclic_motion

Calculate the epicyclic (combined precession + nutation) motion

calculate_limit_cycle_yaw

Calculate the limit cycle yaw angle

calculate_nutation_amplitude

Calculate nutation amplitude with exponential damping

calculate_nutation_frequency

Fast-mode (nutation) angular frequency in rad/s: phi_fast = (Ix p / 2 Iy)(1 + sqrt(1 - 1/Sg)).

calculate_precession_frequency

Slow-mode (precession) angular frequency in rad/s — the slow coning of the spin axis: phi_slow = (Ix p / 2 Iy)(1 - sqrt(1 - 1/Sg)).

epicyclic_frequencies

The two epicyclic yaw-arm angular frequencies (rad/s) for a gyroscopically stable projectile: the FAST mode (nutation) and the SLOW mode (precession). Standard linearized aeroballistic result from the spinning-projectile yaw equation: phi_{fast,slow} = (Ix * p / 2 Iy) * [1 ± sqrt(1 - 1/Sg)] where Ix/Iy are the spin/transverse moments of inertia, p the spin rate, Sg the (dimensionless) gyroscopic stability factor. Returns (0, 0) when Sg <= 1 (no real epicyclic motion — the projectile is not gyroscopically stable) or the transverse inertia is zero. (MBA-941: the previous per-frequency formulas were dimensionally inconsistent — rad/m and length — and ad hoc.)