MATLAB simulation of satellite orientation and rotational stability in Low Earth Orbit using Euler angle dynamics and gravitational effects.
- Satellite orientation changes (roll, pitch, yaw)
- Rotational stability under different conditions
- Gravitational gradient torques
- Momentum wheel desaturation operations
- Angular momentum conservation
Conditions: Zero rotation, no external torques
Result: Perfect stability - all angles remain at 0 radians
Application: Baseline for attitude control system performance
Conditions: Initial rotation (0.1 rad) with angular velocities (p=0.05, q=0.03, r=0.02 rad/s)
Result: Constant spin rates, linear angle increase
Application: Loss of attitude control - demonstrates momentum conservation during wheel failures
Conditions: Small disturbance, gravity torques enabled
Result: Oscillatory "rocking" motion around equilibrium
Application: Passive stabilization - predicts pointing accuracy without active control
Gravity Gradient - Euler Angles: 
Gravity Gradient - Angular Rates:
Conditions: High angular momentum (p=0.1, q=0.08, r=0.05 rad/s), damping torques
Result: Exponential decay of rotation rates over 30 seconds
Reaction Wheel - Euler Angles:
Reaction Wheel - Angular Rates:
Real-World Application: This directly connects to Substack indicator #1 - Momentum Wheel Saturation Creep. When momentum wheels become saturated from accumulated disturbances, operators must dump angular momentum using thrusters. This simulation shows the desaturation maneuver profile. Business Value: Predicting how fast momentum builds up (and how often desaturation is needed) directly impacts:
Propellant budget (each desaturation burns fuel) Mission lifetime (run out of propellant = mission over) Operational planning (when to schedule maneuvers)
Technical Details Physics Engine: Euler's equations of motion for rigid body rotation Governing Equations: phi_dot = p + qsin(phi)tan(theta) + rcos(phi)tan(theta) theta_dot = qcos(phi) - rsin(phi) psi_dot = q*sin(phi)sec(theta) + rcos(phi)*sec(theta) Numerical Integration: MATLAB's ode45 (Runge-Kutta 4th/5th order adaptive method) Satellite Parameters:
Mass: 1000 kg Moments of inertia: I_xx=1000, I_yy=1500, I_zz=800 kg·m² Orbit: 500 km altitude circular LEO
Attitude control failures cause ~15% of satellite mission losses. This simulation:
- Predicts momentum wheel saturation rates
- Designs control budgets (propellant allocation)
- Validates stability margins
- Plans desaturation maneuver sequences
% Run any scenario
main_stable
main_tumbling
main_gravity_gradient
main_reaction_wheelRequirements: MATLAB (base installation only)