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Alfred Lynam March 6, 2008 Dynamics and Control Monte Carlo Preliminary Results

This document presents the preliminary results of a Monte Carlo simulation performed for the Dynamics and Control course in AAE 450. The simulation analyzed a 1 kg case with 115% simulation, running 300 cases with periapses over 300 km. Various input values were determined by the trajectory team, and histograms were created to visualize the variations in periapsis, eccentricity, and specific impulse (Isp) of different stages.

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Alfred Lynam March 6, 2008 Dynamics and Control Monte Carlo Preliminary Results

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  1. Alfred LynamMarch 6, 2008Dynamics and ControlMonte Carlo Preliminary Results AAE 450 Spring 2008 Dynamics and Control

  2. Monte Carlo Results • 1 kg Case 115% Simulation: • 300 Cases run • 300 Cases had periapses of over 300km! • Credit: • Mike Walker and Adam Waite created the code that generated this case. Alfred Lynam ran the Monte Carlo simulation. • Trajectory team determined nominal trajectories. • Entire team determined various code input values. AAE 450 Spring 2008 Dynamics and Control

  3. Periapsis Histogram AAE 450 Spring 2008 Dynamics and Control

  4. Percentage Variations of InputsCredit: MAT AAE 450 Spring 2008 Dynamics and Control

  5. Backup Slides Eccentricity Histogram AAE 450 Spring 2008 Dynamics and Control

  6. Backup Slides Isp of first stage Histogram AAE 450 Spring 2008 Dynamics and Control

  7. Backup Slides Isp of second stage Histogram AAE 450 Spring 2008 5 Dynamics and Control

  8. Backup Slides Isp of third stage Histogram AAE 450 Spring 2008 5 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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