Oscillator1Dof.hpp

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// Vulcan 1-DOF Oscillator Dynamics
// Pure stateless functions for harmonic oscillator computations
#pragma once
 
#include <vulcan/core/VulcanTypes.hpp>
 
#include <janus/janus.hpp>
 
namespace vulcan::dynamics {
 
// =============================================================================
// 1-DOF Harmonic Oscillator Dynamics
// =============================================================================

template <typename Scalar>
Scalar oscillator_acceleration(const Scalar &x, const Scalar &x_dot,
                               const Scalar &omega_n, const Scalar &zeta,
                               const Scalar &force, const Scalar &mass) {
    // ẍ = F/m - 2ζωẋ - ω²x
    return force / mass - Scalar(2) * zeta * omega_n * x_dot -
           omega_n * omega_n * x;
}

template <typename Scalar>
Scalar spring_damper_acceleration(const Scalar &x, const Scalar &x_dot,
                                  const Scalar &stiffness,
                                  const Scalar &damping, const Scalar &force,
                                  const Scalar &mass) {
    // ẍ = (F - c·ẋ - k·x) / m
    return (force - damping * x_dot - stiffness * x) / mass;
}
 
// =============================================================================
// Parameter Conversions
// =============================================================================

template <typename Scalar>
Scalar spring_to_omega(const Scalar &stiffness, const Scalar &mass) {
    return janus::sqrt(stiffness / mass);
}

template <typename Scalar>
Scalar spring_to_zeta(const Scalar &stiffness, const Scalar &damping,
                      const Scalar &mass) {
    return damping / (Scalar(2) * janus::sqrt(stiffness * mass));
}

template <typename Scalar> Scalar oscillator_period(const Scalar &omega_n) {
    return Scalar(2) * Scalar(M_PI) / omega_n;
}
 
// =============================================================================
// Energy Calculations
// =============================================================================

template <typename Scalar>
Scalar oscillator_energy(const Scalar &x, const Scalar &x_dot,
                         const Scalar &omega_n, const Scalar &mass) {
    // E = 0.5*m*ẋ² + 0.5*k*x² = 0.5*m*(ẋ² + ω²x²)
    return Scalar(0.5) * mass * (x_dot * x_dot + omega_n * omega_n * x * x);
}

template <typename Scalar>
Scalar oscillator_kinetic_energy(const Scalar &x_dot, const Scalar &mass) {
    return Scalar(0.5) * mass * x_dot * x_dot;
}

template <typename Scalar>
Scalar oscillator_potential_energy(const Scalar &x, const Scalar &omega_n,
                                   const Scalar &mass) {
    // U = 0.5*k*x² = 0.5*m*ω²*x²
    return Scalar(0.5) * mass * omega_n * omega_n * x * x;
}
 
} // namespace vulcan::dynamics