Aerospace Engineering

# Lift equation
L = 0.5 * rho * V**2 * S * Cl

# Drag equation  
D = 0.5 * rho * V**2 * S * Cd

# Reynolds number (laminar vs turbulent flow)
Re = (rho * V * L) / mu

Where ρ = air density, V = velocity, S = wing area, Cl/Cd = coefficients.

Flight Mechanics

# Thrust required for level flight at constant altitude
TR = W * (Cd0 + (K * Cl**2)) / Cl

# Turn rate for coordinated turn
n = 1 / cos(bank_angle)  # load factor

# Range equation (Breguet)
R = (V / SFC) * (L/D) * ln(W_start / W_end)

Structural Analysis

# Stress-strain relationship (Hooke's Law)
sigma = E * epsilon

# Von Mises stress for yielding criteria
sigma_vm = sqrt(0.5 * ((s1-s2)**2 + (s2-s3)**2 + (s3-s1)**2))

# Factor of Safety
FoS = Ultimate_Stress / Working_Stress

Orbital Mechanics

# Orbital velocity
v = sqrt(mu / r)

# Escape velocity
v_esc = sqrt(2 * mu / r)

# Period of circular orbit
T = 2 * pi * sqrt(a**3 / mu)

Common Software Tools