Albert C Chaney 27 March 2008 Dynamics and

Albert C. Chaney 27 March 2008 Dynamics and Control Simulator Construction Thanks to D&C Team (Everyone) 43 Dtcc AAE 450 Spring 2008

Simulator Construction Ø Blocks 1 and 2 found from nominal trajectory from Trajectory Group ØBlock 3 is controller; compares desired orientation to actual orientation 1 3 2 ØBlock 4 models dynamics of launch vehicle ØBlock 5 is the outputs AAE 450 Spring 2008 Dynamics and Controls 4 5

Controller Design § Nominal Trajectory Position, velocity, and desired orientation § IMU Actual position and velocity § Controller Calculates direction that thrust must be vectored to correct for position and orientation § Made the simulation to act as rocket and IMU to test the controller on AAE 450 Spring 2008 Dynamics and Controls

Definition of Variables § Dtcc = Days to Commissioning and Commencement AAE 450 Spring 2008

Rigid Body FBD and Assumptions cp cm ct 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) alongitudinal axis of spacecraft • Craft is axisymmetric about cm • Everything is a function of time ct AAE 450 Spring 2008 Dynamics and Control

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

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

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

Moment Equations: Aerodynamic AAE 450 Spring 2008 Dynamics and Control

Moment Equations: Thrust AAE 450 Spring 2008

Kinematic Relations Kinematic relations developed by A. Chaney Moments of inertia about principal body axes Equations of motion derived by A. Chaney and J. Stuart AAE 450 Spring 2008