1. 1 AAE 450 Spring 2008 Jeff Stuart 3/20/2008 Dynamics and Controls Spin Stabilization and TVC

2. 2 AAE 450 Spring 2008 Rigid Body Free Body Diagram Dynamics and Controls cp cm ct

3. 3 Spin and TVC Results AAE 450 Spring 2008 Dynamics and Controls Max TVC Angle: 5 deg

4. 4 References Longuski, J.M., Kia, T., and Breckenridge, W.G. “Annihilation of Angular Momentum Bias During Thrusting and Spinning-up Maneuvers” Journal of the Astronautical Sciences, Vol. 37, No. 4, October- December 1989, pp. 433-450. National Association of Rocketry http://www.nar.org/pdf/Estes/E9.pdf Bennett, Ray. The Underachiever’s Manifesto. Chronicle Books, San Francisco, CA. 2006. AAE 450 Spring 2008 Dynamics and Controls

5. 5 Things I wish I had known  How to use Simulink (because it’s easier to use a program when you’ve actually been taught how to use it)  Aristotle quotes: “The mark of an educated individual is to demand no more precision from a subject than the subject itself allows.” “Pleasure in the job puts perfection in the work.”  Methods of quick and effective research  How to play blues guitar AAE 450 Spring 2008 Dynamics and Controls

6. 6 200g Spin Stabilization Plots Thrusting Pointing ErrorSpin Up Pointing Error

7. 7 1kg Spin Stabilization Plots Thrusting Pointing ErrorSpin Up Pointing Error

8. 8 5kg Spin Stabilization Plots Thrusting Pointing ErrorSpin Up Pointing Error

9. 9 Simplified EOMs (Moments about c.m.) 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 AAE 450 Spring 2008 Dynamics and Control

10. 10 AAE 450 Spring 2008 Dynamics and Control Force Equations Displacement Vectors Applied Moment from Spacecraft Stabilization System Aerodynamic Force Definitions

11. 11 Moment Equations: Gravity and Spin AAE 450 Spring 2008 Dynamics and Control Gravity: Spin Stabilization:

12. 12 Moment Equations: Aerodynamic AAE 450 Spring 2008 Dynamics and Control

13. 13 Moment Equations: Thrust AAE 450 Spring 2008

14. 14 Kinematic relations developed by A. Chaney Moments of inertia about principal body axes Kinematic Relations