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Deyst, John, and Jonathan P. How, 16.61 Aerospace Dynamics, Spring 2003. (Massachusetts Institute of Technology: MIT OpenCourseWare), (Accessed 07 Jul, 2010). License: Creative Commons BY-NC-SA

Aerospace Dynamics

Spring 2003

A gyroscope.
A gyroscope, adapted from . (Image courtesy of MIT OCW.)

Course Highlights

This course on Aerospace Dynamics includes a complete set of lecture notes and assignments, as well as an extensive reference reading list. Topics extend to analysis of both aircraft flight dynamics and spacecraft attitude dynamics, based upon presented principles and equations of motion.

Course Description

This undergraduate course builds upon the dynamics content of Unified Engineering, a sophomore course taught in the Department of Aeronautics and Astronautics at MIT. Vector kinematics are applied to translation and rotation of rigid bodies. Newtonian and Lagrangian methods are used to formulate and solve equations of motion. Additional numerical methods are presented for solving rigid body dynamics problems. Examples and problems describe applications to aircraft flight dynamics and spacecraft attitude dynamics.


Prof. Jonathan P. How
Prof. John Deyst
Course Objectives
  1. Review of the basic Newtonian dynamics
    • Focus on 3D motion
    • Gyroscopic and rotational dynamics
    • Formal approaches for handling coordinate transformations
  2. Lagrangian formulation of the equations of motion
  3. Analysis of aircraft flight dynamics and stability
  4. Analysis of spacecraft attitude dynamics


  1. Review of Newtonian dynamics ≈ 6 lectures
  2. Lagrangian dynamics ≈ 6 lectures
  3. Rigid body motions in 3D ≈ 6 lectures
  4. Aircraft/spacecraft dynamics ≈ 6 lectures
    • Midterm exam #1 in class (1 hour) after Lecture 6 (15%)
    • Midterm exam #2 in class (1 hour) after Lecture 14 (20%)
    • Final exam at the end of the semester (30%)
    • Homework - Out Thursdays, due following Thursday at beginning of class (35%)
      Hand-in in class or drop-off at my office. Collaboration: You can discuss problems
      with others, but you are expected to write up and hand in your own work.
    • You will definitely need access to MATLAB®


None required. Lecture notes will be handed out in class. But various books available for reference are:
  1. Meriam and Kraige. Engineering Mechanics - Dynamics. Wiley, 2001.
  2. Hibbeler. Engineering Mechanics - Statics and Dynamics. Prentice Hall.
  3. Beer and Johnston. Vector Mechanics for Engineers. McGraw-Hill.
  4. Greenwood. Principles of Dynamics. 2nd ed. Prentice Hall [RB dynamics].
  5. Williams, Jr. Fundamentals of Applied Dynamics. Wiley, 1996.
  6. Baruh. Analytical Dynamics. McGraw Hill [fairly advanced].
  7. Wells. Schaum's Outline of Lagrangian Dynamics. McGraw-Hill, 1967.
  8. Goldstein. Classical Mechanics. 2nd ed. Addison Wesley [very advanced].

Learning Objectives for Students Graduating from 16.61 will be Able to:

  1. Use methods of vector kinematics to analyze the translation and rotation of rigid bodies - and explain with appropriate visualizations.
  2. Identify appropriate coordinate frames and calculate the transformations between them.
  3. Formulate and solve for the equations of motion using both the Newtonian and Lagrangian formulations.
  4. Use the basic equations of motion to calculate the fundamental flight modes of an aircraft.
  5. Use the basic equations of motion to calculate the attitude motions of a low Earth orbit spacecraft.

Measurable Outcomes for Students Graduating from 16.61 will be Able to:

  1. Derive the equations of motion in accelerating and rotating frames.
  2. Solve for the equations of motion using both the Newtonian and Lagrangian formulations.
  3. Simulate and predict complex dynamic behavior of vehicles such as projectiles, aircraft, and spacecraft.
  4. Use MATLAB® as a tool for matrix manipulations and dynamic simulation.
  5. Linearize the 6DOF motions associated with most dynamic behavior to establish the basic modes of the motion.


      LEC #       TOPICS       ASSIGNMENTS  
      1       Aerospace Dynamics          
      2       Coriolis "Demystified"       HW1 Issued  
      3       Dynamics          
      4       Introduction to Multiple Intermediate Frames       HW1 Due
    HW2 Issued
      5       Momentum, Angular Momentum, and Dynamics of a System of Particles       HW2 Due
    HW3 Issued
      6       Numerical Solution of Nonlinear Differential Equations       HW3 Due  
              Midterm Exam #1          
      7       Lagrange's Equations          
      8       Examples Using Lagrange's Equations

    Examples (from Lagrangian and Hamiltonian Mechanics by M. G. Calkin. River Edge, NJ: World Scientific Publishing Co. Pte. Ltd., 1999.)
          HW4 Issued  
      9       Virtual Work and the Derivation of Lagrange's Equations          
              Virtual Work and the Derivation of Lagrange's Equations (Continued)       HW4 Due
    HW5 Issued
      10       Friction in Lagrange's Equations          
              Friction in Lagrange's Equations (Continued)       HW5 Due
    HW6 Issued
      11       Kinematics of Rigid Bodies          
      12       Rigid Body Dynamics       HW6 Due
    HW7 Issued
      13       Axisymmetric Rotations          
      14       Gyroscopes       HW7 Due
    HW8 Issued
              Gyroscopes (Continued)       HW8 Due  
              Midterm Exam #2       HW9 Issued  
      15       Spacecraft Attitude Dynamics          
              Spacecraft Attitude Dynamics (Continued)       HW9 Due
    HW10 Issued
      16       Aircraft Dynamics          
      17       Aircraft Longitudinal Dynamics       HW10 Due  
      18       Aircraft Lateral Dynamics          
              Final Exam   Tell A Friend