16.07 | Fall 2009 | Undergraduate



Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session

Recitations: 2 sessions / week, 1 hour / session

Course Objectives

Be able to construct idealized (particle and rigid body) dynamical models and predict model response to applied forces using Newtonian mechanics.

Specific Learning Objectives

  • Describe and predict the motion experienced by inertial and non-inertial observers
  • Understand central force motion
  • Understand the basic principles of 2D rigid body motion
  • Formulate the equations of motion of 3D rigid bodies
  • Understand linear theory of harmonic oscillators

Measurable Outcomes

  • Select and use an appropriate coordinate system to describe particle motion
  • Describe particle motion using intermediate reference frames, which can be in relative motion (including rotation) with respect to each other
  • Formulate dynamic models in accelerating frames
  • Identify and exploit situations in which integrated forms of the equations of motion, yielding conservation of momentum and/or energy, can be used
  • Utilize 2-body orbital mechanics to analyze space trajectories
  • Utilize Euler’s equations in body-fitted principal axes
  • Model and analyze simple problems involving vibration with and without damping
  • Develop governing equations of dynamic systems using Lagrange’s equations

Academic Expectations: Collaboration

Adhering to high standards of academic integrity is an important part of your undergraduate experience. The standards are obvious when it comes to exams. Collaboration, such as working with others to conceptualize a problem, define approaches to the solution, or debug code, is often a gray area, and faculty in different courses may have different approaches to this issue.

In this course, collaboration is allowed as long as it is identified. Plagiarism, such as copying someone else’s solution or MATLAB® code, is not allowed. The write-ups must always be your own. Modifying someone else’s code to make it your “own” is unacceptable. In case of doubt, consult the course instructor or the graduate TA.

If you choose to collaborate with other students on the homework problems or the laboratory assignments, indicate their names and the nature of your joint work. Ensure that your collaborator does the same on his/her assignment. A useful discussion of these issues may be found at MIT Academic Integrity.


  • There will be 12 problem sets and 2 laboratory assignments.
  • There will be two midterm quizzes held in recitations.
  • There will be written concept quizzes given in the first 20-25 minutes of each recitation.
  • Concept quizzes will be replaced by small ungraded group oral exams held during three recitations, as listed in the calendar.
  • Attendance is mandatory.
  • There will be a comprehensive final exam during finals week.

Problem Set Policy

Each problem set will typically contain a MATLAB problem. MATLAB programming is not an end in itself but a means to investigate more complex phenomena using numerical methods. The MATLAB code itself is not an adequate solution to the problem; you must interpret your numerical results and answer the questions posed. You should approach the problem with the goal to understand and explain the physical phenomena investigated and the behavior of the system for variations of the parameters.

Submission Checklist

  1. Write up the problem and submit the answers in complete form.
    1. For an answer to be complete, you must explain the method you used to find the solution including the equations needed and explain the setup from the code.
    2. You also must include the solutions that the code generated with the appropriate comments about what these solutions indicate about the question posed.
  2. If it is a MATLAB problem, submit the code that generates the answers available on the course Web site.
  3. Each homework problem must be on a separate sheet of paper. If you need more than one sheet you should staple them together.
  4. Turn paper copies in before class starts on the due date. No late work will be graded.
  5. Submit code through the course Web site, before class starts on the due date.
  6. When collaborating, be sure to write the names of those you are working with on the top of your homework.
    1. Collaboration is not sharing code files or copying someone’s answers.
    2. Collaboration is asking questions to help clarify your own difficulties with the problem set.

Laboratory Assignments

The laboratory assignments involve simulation of orbital mechanical and spacecraft mission planning. The plan for this year’s laboratory assignments is to simulate missions to the moon. They require the use of MATLAB. The required analysis, derivations, results and discussion as well as the requested plots need to be turned in on paper on the due date. The code is not to be turned in on paper. Late assignments will not be accepted.


Problem sets 30%
Concept quizzes 20%
Laboratory assignments 15%
Midterm tests 15%
Final exam 20%

The grade for one problem set and one written concept quiz will be dropped in calculating the final grade.

Course Info