Jeff Stuart 2/14/2008 Dynamics and Controls Spin Stabilization of Third Stage AAE 450 Spring 2008 1

Set-Up and Assumptions Axisymmetric about Distance between cg and cm negligible Out of atmosphere (no drag) Constant mass flow rate Uniform density No initial spin cm S 3rd Stage 2nd Stage Spin Table AAE 450 Spring 2008 2 Dynamics and Controls

Future Work Further investigate spin and thrust vector control 3 AAE 450 Spring 2008 3 Dynamics and Controls

Simplified EOMs Kinematic relations developed by A. Chaney 4 AAE 450 Spring 2008 4 Dynamics and Controls

Spin rate in terms of time Solution Derivation – Spin-up before engine ignition Spin rate in terms of time AAE 450 Spring 2008 5 Dynamics and Controls

Scaled Vanguard Data From C. Strauss 6 Dynamics and Controls AAE 450 Spring 2008 6 Dynamics and Controls

References Schmidt, James. “Performance of X 258 Third-Stage Motor on Delta 36 (OT-3)”. NASA Report. July 1967 GPS IIR-12 Media Kit. The Boeing Company. 6/6/2005 http://www.boeing.com/defense-space/space/delta/kits/d305_gps_iir-12.pdf AAE 450 Spring 2008 7 Dynamics and Controls