1. Jeff Stuart 1/31/2008 Dynamics and Control Simplified Rigid Body Equations of Motion
AAE 450 Spring 2008

2. Rigid Body FBD and Assumptions
ωi : angular velocity about
Ii : moment of inertia about
Simplifying Assumptions:
No Lift Force
Drag force has no component
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
frame is “inertial”
AAE 450 Spring 2008
Dynamics and Control

3. Simplified EOMs (Moments about c.m.)
Kinematic relations developed by A. Chaney
Inputs from other sub-teams:
Aerothermal: Aerodynamic force models, cp
Propulsion: Thrust model, thrust vectoring, ct
Structures: Inertia matrix, cm
Trajectory: Nominal trajectory
Future Work
Generalize EOMs further
Develop basic controller
AAE 450 Spring 2008
Dynamics and Control

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

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

6. Moment Equations: Lift and Drag
AAE 450 Spring 2008
Dynamics and Control

7. Moment Equations: Thrust
AAE 450 Spring 2008