ballistics_engine/

precession_nutation.rs

//! 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

// Precession and nutation modeling - now integrated!

use crate::pitch_damping::{
    calculate_pitch_damping_moment,
    PitchDampingCoefficients,
};

/// Complete angular state of the projectile
#[derive(Debug, Clone, Copy)]
pub struct AngularState {
    pub pitch_angle: f64,      // Angle between axis and velocity (rad)
    pub yaw_angle: f64,        // Angle in plane perpendicular to velocity (rad)
    pub pitch_rate: f64,       // Rate of pitch angle change (rad/s)
    pub yaw_rate: f64,         // Rate of yaw angle change (rad/s)
    pub precession_angle: f64, // Cumulative precession angle (rad)
    pub nutation_phase: f64,   // Phase of nutation oscillation (rad)
}

/// Parameters for precession and nutation calculations
#[derive(Debug, Clone)]
pub struct PrecessionNutationParams {
    // Projectile properties
    pub mass_kg: f64,
    pub caliber_m: f64,
    pub length_m: f64,
    pub spin_rate_rad_s: f64,
    
    // Moments of inertia
    pub spin_inertia: f64,      // About longitudinal axis
    pub transverse_inertia: f64, // About transverse axis
    
    // Flight conditions
    pub velocity_mps: f64,
    pub air_density_kg_m3: f64,
    pub mach: f64,
    
    // Damping coefficients
    pub pitch_damping_coeff: f64,
    pub nutation_damping_factor: f64, // Fraction of critical damping
}

impl Default for PrecessionNutationParams {
    fn default() -> Self {
        Self {
            mass_kg: 0.01134,  // 175 grains
            caliber_m: 0.00782,
            length_m: 0.033,
            spin_rate_rad_s: 17522.0,
            spin_inertia: 6.94e-8,
            transverse_inertia: 9.13e-7,
            velocity_mps: 850.0,
            air_density_kg_m3: 1.225,
            mach: 2.48,
            pitch_damping_coeff: -0.8,
            nutation_damping_factor: 0.05,
        }
    }
}

/// Calculate the natural precession frequency
pub fn calculate_precession_frequency(
    spin_rate_rad_s: f64,
    velocity_mps: f64,
    spin_inertia: f64,
    transverse_inertia: f64,
    yaw_angle_rad: f64,
) -> f64 {
    if velocity_mps == 0.0 || transverse_inertia == 0.0 {
        return 0.0;
    }
    
    // Basic gyroscopic precession
    // ωp = (Is * ωs * sin(α)) / (It * V)
    (spin_inertia * spin_rate_rad_s * yaw_angle_rad.sin()) / 
        (transverse_inertia * velocity_mps)
}

/// Calculate the natural nutation frequency
pub fn calculate_nutation_frequency(
    spin_rate_rad_s: f64,
    spin_inertia: f64,
    transverse_inertia: f64,
    stability_factor: f64,
) -> f64 {
    if stability_factor <= 1.0 || transverse_inertia == 0.0 {
        return 0.0;
    }
    
    // Nutation frequency
    // ωn = ωs * sqrt(Is / It) * sqrt(Sg - 1)
    let inertia_ratio = spin_inertia / transverse_inertia;
    spin_rate_rad_s * inertia_ratio.sqrt() * (stability_factor - 1.0).sqrt()
}

/// Calculate nutation amplitude with exponential damping
pub fn calculate_nutation_amplitude(
    initial_disturbance_rad: f64,
    time_s: f64,
    nutation_frequency: f64,
    damping_factor: f64,
    spin_rate_rad_s: f64,
) -> f64 {
    if nutation_frequency == 0.0 || spin_rate_rad_s == 0.0 {
        return 0.0;
    }
    
    // Damping rate
    let damping_rate = damping_factor * nutation_frequency;
    
    // Exponential decay
    let amplitude = initial_disturbance_rad * (-damping_rate * time_s).exp();
    
    // Clamp to reasonable bounds
    amplitude.min(0.1) // Max 0.1 rad (~5.7 degrees)
}

/// Calculate the combined precession and nutation motion
pub fn calculate_combined_angular_motion(
    params: &PrecessionNutationParams,
    angular_state: &AngularState,
    time_s: f64,
    dt: f64,
    initial_disturbance: f64,
) -> AngularState {
    // Calculate stability factor (simplified)
    let stability = (params.spin_inertia * params.spin_rate_rad_s.powi(2)) / 
        (4.0 * params.transverse_inertia * params.velocity_mps.powi(2) / params.length_m);
    
    // Precession frequency
    let omega_p = calculate_precession_frequency(
        params.spin_rate_rad_s,
        params.velocity_mps,
        params.spin_inertia,
        params.transverse_inertia,
        angular_state.yaw_angle,
    );
    
    // Nutation frequency
    let omega_n = calculate_nutation_frequency(
        params.spin_rate_rad_s,
        params.spin_inertia,
        params.transverse_inertia,
        stability,
    );
    
    // Nutation amplitude (decaying)
    let nutation_amp = calculate_nutation_amplitude(
        initial_disturbance,
        time_s,
        omega_n,
        params.nutation_damping_factor,
        params.spin_rate_rad_s,
    );
    
    // Update precession angle
    let new_precession_angle = angular_state.precession_angle + omega_p * dt;
    
    // Update nutation phase
    let new_nutation_phase = angular_state.nutation_phase + omega_n * dt;
    
    // Calculate pitch damping moment
    let pitch_moment = calculate_pitch_damping_moment(
        angular_state.pitch_rate,
        params.velocity_mps,
        params.air_density_kg_m3,
        params.caliber_m,
        params.length_m,
        params.mach,
        &PitchDampingCoefficients {
            subsonic: params.pitch_damping_coeff,
            ..Default::default()
        },
    );
    
    // Angular acceleration from damping
    let pitch_accel = pitch_moment / params.transverse_inertia;
    
    // Update angular rates
    let new_pitch_rate = angular_state.pitch_rate + pitch_accel * dt;
    let new_yaw_rate = omega_p; // Precession rate
    
    // Combined angle with nutation
    // The total yaw is precession + nutation oscillation
    let total_yaw = angular_state.yaw_angle + nutation_amp * new_nutation_phase.sin();
    
    // Pitch angle evolves more slowly
    let new_pitch = angular_state.pitch_angle + new_pitch_rate * dt;
    
    AngularState {
        pitch_angle: new_pitch,
        yaw_angle: total_yaw,
        pitch_rate: new_pitch_rate,
        yaw_rate: new_yaw_rate,
        precession_angle: new_precession_angle,
        nutation_phase: new_nutation_phase,
    }
}

/// Calculate the epicyclic (combined precession + nutation) motion
pub fn calculate_epicyclic_motion(
    spin_rate_rad_s: f64,
    velocity_mps: f64,
    stability_factor: f64,
    time_s: f64,
    initial_yaw_rad: f64,
) -> (f64, f64) {
    if stability_factor <= 1.0 {
        // Unstable - no regular motion
        return (initial_yaw_rad, initial_yaw_rad);
    }
    
    // Frequencies (simplified model)
    // Slow mode (precession)
    let omega_slow = 2.0 * velocity_mps / (stability_factor * spin_rate_rad_s);
    
    // Fast mode (nutation)
    let omega_fast = spin_rate_rad_s * ((stability_factor - 1.0).sqrt()) / stability_factor;
    
    // Amplitude ratio (fast/slow)
    let amplitude_ratio = 1.0 / stability_factor;
    
    // Damping (exponential decay of fast mode)
    let damping_factor = 0.1; // Typical value
    let fast_amplitude = amplitude_ratio * (-damping_factor * omega_fast * time_s).exp();
    
    // Combined motion
    let slow_phase = omega_slow * time_s;
    let fast_phase = omega_fast * time_s;
    
    // Epicyclic coordinates
    let yaw = initial_yaw_rad * (slow_phase.cos() + fast_amplitude * fast_phase.cos());
    let pitch = initial_yaw_rad * (slow_phase.sin() + fast_amplitude * fast_phase.sin());
    
    (pitch, yaw)
}

/// Calculate the limit cycle yaw angle
pub fn calculate_limit_cycle_yaw(
    velocity_mps: f64,
    _spin_rate_rad_s: f64,
    stability_factor: f64,
    crosswind_mps: f64,
) -> f64 {
    // Base yaw from crosswind
    let wind_yaw = if crosswind_mps != 0.0 && velocity_mps > 0.0 {
        (crosswind_mps / velocity_mps).atan()
    } else {
        0.0
    };
    
    // Yaw of repose (equilibrium)
    let yaw_of_repose = if stability_factor > 1.0 {
        // Typical value for spin-stabilized projectiles
        let repose_factor = 1.0 / (1.0 + 0.5 * (stability_factor - 1.0));
        0.002 * repose_factor // ~0.1 degrees nominal
    } else {
        0.01 // Larger for marginally stable
    };
    
    wind_yaw + yaw_of_repose
}

#[cfg(test)]
mod tests {
    use super::*;
    
    #[test]
    fn test_precession_frequency() {
        let freq = calculate_precession_frequency(
            17522.0,  // spin rate
            850.0,    // velocity
            6.94e-8,  // spin inertia
            9.13e-7,  // transverse inertia
            0.002,    // yaw angle
        );
        
        // Should be small for small yaw angles
        assert!(freq.abs() < 1.0);
    }
    
    #[test]
    fn test_nutation_frequency() {
        let freq = calculate_nutation_frequency(
            17522.0,  // spin rate
            6.94e-8,  // spin inertia
            9.13e-7,  // transverse inertia
            1.5,      // stability
        );
        
        // Should be in the kHz range
        assert!(freq > 1000.0);
        assert!(freq < 10000.0);
    }
    
    #[test]
    fn test_nutation_damping() {
        let initial = 0.01;
        let freq = 3000.0;
        
        // Check exponential decay
        let amp_0 = calculate_nutation_amplitude(initial, 0.0, freq, 0.05, 17522.0);
        let amp_1 = calculate_nutation_amplitude(initial, 0.1, freq, 0.05, 17522.0);
        
        assert_eq!(amp_0, initial);
        assert!(amp_1 < amp_0);
        assert!(amp_1 > 0.0);
    }
    
    #[test]
    fn test_precession_edge_cases() {
        // Test zero velocity
        let freq_zero_vel = calculate_precession_frequency(
            17522.0, 0.0, 6.94e-8, 9.13e-7, 0.002
        );
        assert_eq!(freq_zero_vel, 0.0);
        
        // Test zero transverse inertia
        let freq_zero_inertia = calculate_precession_frequency(
            17522.0, 850.0, 6.94e-8, 0.0, 0.002
        );
        assert_eq!(freq_zero_inertia, 0.0);
        
        // Test zero yaw angle (sin(0) = 0)
        let freq_zero_yaw = calculate_precession_frequency(
            17522.0, 850.0, 6.94e-8, 9.13e-7, 0.0
        );
        assert_eq!(freq_zero_yaw, 0.0);
    }
    
    #[test]
    fn test_nutation_edge_cases() {
        // Test unstable projectile (Sg <= 1)
        let freq_unstable = calculate_nutation_frequency(
            17522.0, 6.94e-8, 9.13e-7, 0.9
        );
        assert_eq!(freq_unstable, 0.0);
        
        // Test marginally stable (Sg = 1)
        let freq_marginal = calculate_nutation_frequency(
            17522.0, 6.94e-8, 9.13e-7, 1.0
        );
        assert_eq!(freq_marginal, 0.0);
        
        // Test zero transverse inertia
        let freq_zero_inertia = calculate_nutation_frequency(
            17522.0, 6.94e-8, 0.0, 2.0
        );
        assert_eq!(freq_zero_inertia, 0.0);
    }
    
    #[test]
    fn test_nutation_amplitude_bounds() {
        let initial = 0.5; // Large initial disturbance
        let freq = 3000.0;
        let spin = 17522.0;
        
        // Even with large initial disturbance, should be clamped
        let amp = calculate_nutation_amplitude(initial, 0.0, freq, 0.05, spin);
        assert!(amp <= 0.1); // Max 0.1 rad
        
        // Test zero frequency
        let amp_zero_freq = calculate_nutation_amplitude(initial, 1.0, 0.0, 0.05, spin);
        assert_eq!(amp_zero_freq, 0.0);
        
        // Test zero spin
        let amp_zero_spin = calculate_nutation_amplitude(initial, 1.0, freq, 0.05, 0.0);
        assert_eq!(amp_zero_spin, 0.0);
    }
    
    #[test]
    fn test_epicyclic_motion() {
        let (pitch, yaw) = calculate_epicyclic_motion(
            17522.0,  // spin rate
            850.0,    // velocity
            2.5,      // stability factor
            0.1,      // time
            0.01      // initial yaw
        );
        
        // Should produce reasonable angles
        assert!(pitch.abs() <= 0.01);
        assert!(yaw.abs() <= 0.01);
        
        // Test unstable case
        let (pitch_unstable, yaw_unstable) = calculate_epicyclic_motion(
            17522.0, 850.0, 0.9, 0.1, 0.01
        );
        assert_eq!(pitch_unstable, 0.01);
        assert_eq!(yaw_unstable, 0.01);
    }
    
    #[test]
    fn test_limit_cycle_yaw() {
        // Test with crosswind
        let yaw_wind = calculate_limit_cycle_yaw(
            850.0,    // velocity
            17522.0,  // spin rate
            2.5,      // stability
            10.0      // crosswind
        );
        
        // Should be small but non-zero
        assert!(yaw_wind > 0.0);
        assert!(yaw_wind < 0.1);
        
        // Test without crosswind
        let yaw_no_wind = calculate_limit_cycle_yaw(
            850.0, 17522.0, 2.5, 0.0
        );
        assert!(yaw_no_wind > 0.0);
        assert!(yaw_no_wind < yaw_wind);
        
        // Test unstable projectile
        let yaw_unstable = calculate_limit_cycle_yaw(
            850.0, 17522.0, 0.9, 0.0
        );
        assert_eq!(yaw_unstable, 0.01); // Fixed value for unstable
    }
    
    #[test]
    fn test_combined_angular_motion() {
        let params = PrecessionNutationParams::default();
        let initial_state = AngularState {
            pitch_angle: 0.001,
            yaw_angle: 0.002,
            pitch_rate: 0.01,
            yaw_rate: 0.01,
            precession_angle: 0.0,
            nutation_phase: 0.0,
        };
        
        let new_state = calculate_combined_angular_motion(
            &params,
            &initial_state,
            0.1,  // time
            0.001, // dt
            0.001  // initial disturbance
        );
        
        // Check that nutation phase evolved (it always should with non-zero frequency)
        // Precession might be very small with small yaw angles
        assert!(new_state.nutation_phase != initial_state.nutation_phase || 
                new_state.precession_angle != initial_state.precession_angle);
        
        // Check reasonable bounds
        assert!(new_state.pitch_angle.abs() < 1.0);
        assert!(new_state.yaw_angle.abs() < 1.0);
    }
    
    #[test]
    fn test_default_params() {
        let params = PrecessionNutationParams::default();
        
        // Check reasonable default values
        assert!(params.mass_kg > 0.0);
        assert!(params.caliber_m > 0.0);
        assert!(params.length_m > 0.0);
        assert!(params.spin_rate_rad_s > 0.0);
        assert!(params.spin_inertia > 0.0);
        assert!(params.transverse_inertia > 0.0);
        assert!(params.velocity_mps > 0.0);
        assert!(params.air_density_kg_m3 > 0.0);
        assert!(params.mach > 0.0);
        assert!(params.nutation_damping_factor > 0.0);
        assert!(params.nutation_damping_factor < 1.0); // Should be fraction
    }
    
    #[test]
    fn test_stability_effects() {
        // High stability should give lower frequencies
        let freq_high_stability = calculate_nutation_frequency(
            17522.0, 6.94e-8, 9.13e-7, 5.0
        );
        
        let freq_low_stability = calculate_nutation_frequency(
            17522.0, 6.94e-8, 9.13e-7, 1.5
        );
        
        // Higher stability gives higher nutation frequency
        assert!(freq_high_stability > freq_low_stability);
    }
    
    #[test]
    fn test_damping_time_evolution() {
        let initial = 0.01;
        let freq = 3000.0;
        let spin = 17522.0;
        let damping = 0.1;
        
        // Sample at different times
        let times = [0.0, 0.01, 0.02, 0.05, 0.1, 0.2];
        let mut last_amp = initial;
        
        for &t in &times[1..] {
            let amp = calculate_nutation_amplitude(initial, t, freq, damping, spin);
            
            // Should monotonically decrease
            assert!(amp < last_amp);
            assert!(amp >= 0.0);
            last_amp = amp;
        }
    }
    
    #[test]
    fn test_angular_state_evolution() {
        let params = PrecessionNutationParams {
            mass_kg: 0.01,
            caliber_m: 0.008,
            length_m: 0.03,
            spin_rate_rad_s: 10000.0,
            spin_inertia: 5e-8,
            transverse_inertia: 8e-7,
            velocity_mps: 800.0,
            air_density_kg_m3: 1.2,
            mach: 2.3,
            pitch_damping_coeff: -0.5,
            nutation_damping_factor: 0.08,
        };
        
        let mut state = AngularState {
            pitch_angle: 0.0,
            yaw_angle: 0.005,
            pitch_rate: 0.0,
            yaw_rate: 0.0,
            precession_angle: 0.0,
            nutation_phase: 0.0,
        };
        
        // Store initial state for comparison
        let initial_phase = state.nutation_phase;
        let initial_precession = state.precession_angle;
        
        // Evolve for several timesteps
        let dt = 0.0001;
        for i in 0..100 {
            let time = i as f64 * dt;
            state = calculate_combined_angular_motion(
                &params,
                &state,
                time,
                dt,
                0.002
            );
        }
        
        // Should have evolved - at least one of these should change
        assert!(state.precession_angle != initial_precession || 
                state.nutation_phase != initial_phase);
        
        // Should remain bounded
        assert!(state.yaw_angle.abs() < 0.1);
        assert!(state.pitch_angle.abs() < 0.1);
    }
}