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Alfred Lynam March 27, 2008 Dynamics and Control Monte Carlo Method/Results

Alfred Lynam March 27, 2008 Dynamics and Control Monte Carlo Method/Results. Dynamics and Control. Monte Carlo Simulation Method. Flow Chart by: Mike Walker. AAE 450 Spring 2008. 2. Dynamics and Control. Monte Carlo Results. 200 g Case 145% Simulation: 10000* Cases run

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Alfred Lynam March 27, 2008 Dynamics and Control Monte Carlo Method/Results

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  1. Alfred LynamMarch 27, 2008Dynamics and ControlMonte Carlo Method/Results AAE 450 Spring 2008 Dynamics and Control

  2. Monte Carlo Simulation Method Flow Chart by: Mike Walker AAE 450 Spring 2008 2 Dynamics and Control

  3. Monte Carlo Results • 200 g Case 145% Simulation: • 10000* Cases run • 9999 Cases had periapses of over 300 km • 1 kg Case 115% Simulation: • 10000 Cases run • 9999 Cases had periapses of over 300km • 5 kg Case 125% Simulation: • 10000* Cases run • 10000 Cases had periapses of over 300km * More than 10000 cases were run, but only 10000 were actually analyzed for uniformity. None of the excess cases failed. AAE 450 Spring 2008 Dynamics and Control

  4. Periapsis Histograms 200g Periapsis altitude histogram with a 21.803 km standard deviation and a 437.44 km average. (Alfred Lynam) 1kg Periapsis altitude histogram with a 15.774 km standard deviation and a 367.727 km average. (Alfred Lynam) 5kg periapsis histogram with a 20.215 km standard deviation and a 516.546 km average. (Alfred Lynam) AAE 450 Spring 2008 Dynamics and Control

  5. Eccentricity Histograms 200g Eccentricity histogram with a .0467 standard deviation and a .438 average. (Alfred Lynam) 1kg eccentricity histogram with a .041094 standard deviation and a .173289 average. (Alfred Lynam) Figure A.3.2.8.4.2: 5kg eccentricity histogram with a .050 standard deviation and a .445 average. (Alfred Lynam) AAE 450 Spring 2008 Dynamics and Control

  6. AAE 450 Spring 2008 Dynamics and Control

  7. AAE 450 Spring 2008 Dynamics and Control

  8. AAE 450 Spring 2008 Dynamics and Control

  9. Rigid Body FBD and Assumptions(Jeff Stuart) • Simplifying Assumptions: • Center of gravity is the same as center of mass • Center of mass (cm), center of pressure (cp), and center of thrust (ct) along longitudinal axis of spacecraft • Craft is axisymmetric about cm • Everything is a function of time cp cm ct ct AAE 450 Spring 2008 Dynamics and Control

  10. Simplified EOMs (Moments about c.m.)(Jeff Stuart) AAE 450 Spring 2008 Dynamics and Control

  11. Force Equations(Jeff Stuart) Aerodynamic Force Definitions Applied Moment from Spacecraft Stabilization System Displacement Vectors AAE 450 Spring 2008 Dynamics and Control

  12. Moment Equations: Gravity and Spin(Jeff Stuart) Gravity: Spin Stabilization: AAE 450 Spring 2008 Dynamics and Control

  13. Moment Equations: Aerodynamic(Jeff Stuart) AAE 450 Spring 2008 Dynamics and Control

  14. Moment Equations: Thrust (Jeff Stuart) AAE 450 Spring 2008

  15. Kinematic Relations(Jeff Stuart) Kinematic relations developed by A. Chaney Moments of inertia about principal body axes

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