2.003J | Fall 2007 | Undergraduate

Dynamics and Control I


Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Recitations: 1 session / week, 1 hour / session

MATLAB® Sessions: 1 session / week, 1 hour / session

Course Goals

This version of the class stresses kinematics and builds around a strict but powerful approach to kinematic formulation which is different from the more traditional approach presented in Spring 2007.

Our notation was adapted from that of Professor Kane of Stanford University. We use strict frames, a strict notation for relative velocities and accelerations, frame-oriented derivates of vectors, and a constructive approach to the derivation of linear and angular velocities and accelerations.

Course Materials

Required Text

Williams, J. H., Jr. Fundamentals of Applied Dynamics. New York, NY: John Wiley and Sons, Inc., 2006. ISBN: 9780470133859.

Meriam, J. L., and L. G. Kraige. Engineering Mechanics: Dynamics. 5th ed. Vol. 2. New York, NY: J. Wiley & Sons, 2001. ISBN: 9780471406457.

Class Meetings

Course Structure

Each week, there will be two class lectures, one MATLAB® session, and one recitation.

  • Lectures will be held for 90-minute periods twice per week. Lecture attendance is mandatory. Attendance and participation will be part of the grade.
  • You will be assigned to a MATLAB session that meets once per week, covering material relevant to the course and problem sets. These sessions are a mix of lecture and hands-on lab activities.
  • The purpose of the recitations is to give students experience in the subject by working out examples and expanding on the material presented in the lectures. Attendance and participation in the recitations is mandatory.

Problem Sets

There will be two types of problem sets, one for the dynamics part and one for the MATLAB part. Dynamics problem sets will typically be assigned on Mondays and due the next Monday. They are available in the assignments section. To receive credit, problem sets must be handed in at the beginning of class on the due date. Because of holidays, tests, etc., some problem sets may be provided and will be due on days other than Mondays for some weeks. For the same reason, they may not be assigned for a particular week. Late problem sets will not be accepted. MATLAB problem sets will be handed out during MATLAB sessions and will be due in class on the due-date.

Honesty on Problem Sets

You are welcome, and encouraged, to work on the assignment problems with fellow students. A good way to learn the material is in small study groups. Such groups work best if members have attempted the problems individually before meeting as a group. Of course, the assignment solution that you turn in should reflect your own understanding, and not that of your fellow students. In other words, do not copy directly from other students. If it is obvious that such direct copying has occurred, we will disallow that homework.


  • There will be two in-class mid-term exams. They are scheduled for:
    • Wednesday, Lec #13
    • Monday, Lec #19
  • The 3-hour final exam will be scheduled by the Registrar’s Office.
  • All the exams (including the final) will be closed book. One sheet of handwritten notes will be allowed at the first mid-term exam, two sheets at the second mid-term exam, and three sheets at the final exam.
  • There will be two optional review sessions before each mid-term exam.



Homework and classwork

Homework and classwork include:

  • Dynamics problems due in lecture - 10%
  • Recitation - 7%
  • MATLAB problems - 15%
  • Class participation - 3%

Two mid-term exams 40%
Final exam 25%

Lecture Calendar


I. Motion of a single particle

Kinematics: Frames, transforming between frames, derivatives of vectors, velocity, acceleration, angular velocity, angular acceleration, centripetal terms, Coriolis terms


II. 2D Motion of system of particles

Dynamics: Linear momentum principle, angular momentum principle for system of particles, 2D motion of rigid body: Momentum principles, inertia tensor, parallel axes theorem, instantaneous center of rotation, work-energy principle; variable mass systems

13 Exam 1
14-18, 20

III. Introduction to Lagrangian dynamics

Generalized coordinates and forces; Lagrangian equations of motion for 2D holonomic systems of particles and rigid bodies. Helicopter dynamics

19 Exam 2

IV. Vibrations

Phase plots, equilibria, linearization, stability. 1-DOF oscillations: natural frequencies, free-, damped-, and forced response; time response, frequency response, bode plots

26 Recap
27 Final exam
Learning Resource Types
Lecture Videos
Problem Sets
Programming Assignments with Examples
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