AAE 44000: Spacecraft Attitude Dynamics

Credits:     3

Contact hours:     3

Instructor:     Professor Howell

Text:     No text; Supplemental notes furnished by instructor

Course Description:     The development of spacecraft rigid body equations of motion in terms of direction cosines, angles and quaternions, with external torques. Determination of the attitude stability of the resulting rotational motion of the spacecraft. Stabilization techniques presented and the impact determined through numerical simulations. Introduction to attitude control.

Offered:    Spring

Pre-requisite:    AAE 34000

Co-requisite:    None

Required:    Yes

Student Learning Outcomes:
On completing this course the student shall be able to:

  1. Acquire and apply basic technical knowledge about vehicle orientation
  2. Develop intuition about natural spacecraft attitude motion
  3. Introduction to the dynamical basis for attitude control
  4. Extensive computational analysis and interpretation of results
  5. Communication of the analysis techniques and written interpretation of their own results
  6. Explore spin stabilization of a satellite by designing a rotor to accomplish a specific stability objective

Relationship of Course to Program Outcomes

    Program Learning Outcomes Included?
a An ability to apply knowledge of mathematics, science, and engineering Yes
b An ability to design and conduct experiments, as well as to analyze and interpret data Yes
c An ability to design an aerospace system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health, and safety, manufacturability, and sustainability Yes
d An ability to function on multidisciplinary teams No
e An ability to identify, formulate, and solve aerospace engineering problems Yes
f An understanding of professional and ethical responsibility Yes
g An ability to communicate effectively Yes
h An understanding of the impact of engineering solutions in a global, economic, environmental, and societal context No
i A recognition of the need for, and an ability to engage in life-long learning Yes
j A knowledge of contemporary issues in aerospace engineering Yes
k An ability to use the techniques, skills and modern engineering tools necessary for aerospace engineering practice Yes


  1. Introduction to modern spacecraft dynamics (background and motivation)
  2. Fundamental concepts including the mathematical formalism of dyadics and the mechanics of energy and angular momentum; rotational kinematics including direction cosines, Euler angles, and Euler parameters (quaternions) as kinematic variables; coordinate systems and transformations, angular velocity and kinematic differential equations
  3. Gravitational interactions between particles and bodies; center of gravity and centrobaric bodies
  4. External Torques on a spacecraft details of gravity torques
  5. Simple spacecraft (axisymmetric and unsymmetric) and dynamic differential equations. Torque-free rotational motion; stability analysis; impact of external torques; spin stabilization; gravity gradient stabilization; dual-spinners; mass movement and momentum exchange techniques (momentum wheels, reaction wheels, control moment gyros); three-axis stabilization
  6. Depending on the launch schedules during the current semester, the projects/homework are correlated to actual spacecraft/missions. Previous missions are used as examples as well.

Revision History:
Prepared by: Kathleen C Howell, Date: August 21, 2000
Revised by: Kathleen C. Howell, Date: July 17, 2006
Pre-Req reconciled with Banner: Lisa Crain, Date: October 15, 2010
Format updated: Kathleen C. Howell, February 17, 2012