Physics MCP Server

Uses numerical integration (RK4) to solve motion equations with:
- Quadratic drag force: F_drag = 0.5 * ρ * v² * Cd * A
- Magnus force (spin effects): F_magnus = 0.5 * ρ * Cl * A * ω * r * v
- Wind effects (constant wind vector)
- Variable air density (altitude and temperature effects)

This provides REALISTIC trajectories for sports balls, projectiles,
and other objects moving through air or water. Compare with
calculate_projectile_motion (no drag) to see dramatic differences!

Common drag coefficients (Cd):
    - Sphere: 0.47 (default)
    - Baseball: 0.4
    - Golf ball: 0.25 (dimples reduce drag)
    - Football (American): 0.05-0.15 (orientation-dependent)
    - Basketball: 0.55
    - Soccer ball: 0.25
    - Skydiver (belly-down): 1.0-1.3
    - Streamlined car: 0.25-0.35

Args:
    initial_velocity: Launch velocity in m/s
    angle_degrees: Launch angle in degrees (0-90)
    mass: Object mass in kg
    cross_sectional_area: Cross-section perpendicular to motion in m²
    initial_height: Launch height in meters (default 0)
    drag_coefficient: Drag coefficient Cd (default 0.47 for sphere)
    fluid_density: Fluid density in kg/m³ (air=1.225, water=1000)
    gravity: Gravitational acceleration m/s² (default 9.81)
    time_step: Integration time step in seconds (default 0.01)
    max_time: Maximum simulation time in seconds (default 30)
    spin_rate: Spin rate in rad/s for Magnus force (default 0, no spin)
    spin_axis: Spin axis unit vector [x, y, z] (default [0, 0, 1] = vertical)
    wind_velocity: Wind velocity [vx, vy] in m/s (default [0, 0], no wind)
    altitude: Altitude above sea level in meters (default 0, affects air density)
    temperature: Air temperature in Celsius (default 15, affects air density)

Returns:
    Dict containing:
        - max_height: Maximum altitude reached (m)
        - range: Horizontal distance traveled (m)
        - time_of_flight: Total flight time (s)
        - impact_velocity: Speed at landing (m/s)
        - impact_angle: Angle at landing (degrees below horizontal)
        - trajectory_points: [[x, y], ...] for plotting
        - energy_lost_to_drag: Energy dissipated by drag (J)
        - initial_kinetic_energy: Initial KE (J)
        - final_kinetic_energy: Final KE (J)
        - lateral_deflection: Lateral deflection from spin/wind (m)
        - magnus_force_max: Maximum Magnus force magnitude (N)
        - wind_drift: Total wind drift (m)
        - effective_air_density: Effective air density used (kg/m³)

Example - Baseball curveball (2500 rpm backspin):
    result = await calculate_projectile_with_drag(
        initial_velocity=40.23,  # 90 mph
        angle_degrees=10,
        mass=0.145,
        cross_sectional_area=0.0043,
        drag_coefficient=0.4,
        spin_rate=261.8,  # 2500 rpm = 261.8 rad/s
        spin_axis=[0, 0, 1]  # Backspin (vertical axis)
    )
    # Backspin increases range and height!

Example - Golf ball at altitude (Denver, 1600m):
    result = await calculate_projectile_with_drag(
        initial_velocity=70,
        angle_degrees=12,
        mass=0.0459,
        cross_sectional_area=0.00143,
        drag_coefficient=0.25,
        altitude=1600,  # Denver elevation
        temperature=20  # Summer day
    )
    # Less air resistance = longer drive!

Example - Soccer free kick with wind:
    result = await calculate_projectile_with_drag(
        initial_velocity=25,
        angle_degrees=15,
        mass=0.43,
        cross_sectional_area=0.0388,
        drag_coefficient=0.25,
        wind_velocity=[5, 0],  # 5 m/s tailwind
        spin_rate=50,  # Sidespin for curve
        spin_axis=[0, 1, 0]  # Horizontal axis
    )
    # Wind drift + Magnus curve!