Syllabus

Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Recitations: 1 session / week, 1 hour / session

Laboratories: 1 session / week, 1 hour / session

Description

We will start by applying Newton's Laws and Work-Energy principles to the motion of single particles, systems of particles and rigid bodies in planar motion. Then we use virtual displacements and virtual work to introduce Lagrange's formulation of the equations motion for systems of particles and rigid bodies in planar motion. We will uncover a system's equilibrium points and perform linear stability analyses. Lastly, we consider free and forced vibrations of linear multi-degree of freedom models of mechanical systems. Throughout the course, we will use MATLAB® to practice numerical methods for solving dynamics and vibrations problems.

Goals

After this course you will be able to:

• Apply knowledge of 8.01 and 18.03 to new problems
• Define a coordinate system for the system under consideration
• Derive equations of motion using either Newton's momentum principles or Lagrange's equations
• Analyze the equations of motion for the existence of equilibrium points and characterize the stability of those points
• Solve the equations of motion

Prerequisites

The prerequisites are Physics I (8.01) and Differential Equations (18.03).

Related Courses

After this course, related courses include:

2.004 - Dynamics and Control II

2.050J/12.006J/18.353J - Nonlinear Dynamics I: Chaos

2.032 - Dynamics

Required Texts

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

Recommended Texts

Bedford, A., and Wallace L. Fowler. Engineering Mechanics: Dynamics. 2nd ed. Menlo Park, CA: Addison-Wesley Publishing, Inc., 1998. ISBN: 9780201180718.

Examinations

There will be two mid-term exams (1.5 hours each) scheduled 2 days after Ses #L12 and 5 days after Ses #L19. The final exam is 3 hours long.

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, one before each mid-term exam.

Recitations

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 obligatory.

MATLAB®

There will be MATLAB® sessions on Friday, covering material relevant to the course and problem sets. In addition there will be MATLAB® office hours to help with the homework materials. Typically, the MATLAB® problem to be worked through on Friday will be distributed through the course website earlier in the week.

Homework

Homework problems will typically be assigned every Monday and will be due at the beginning of lecture on Monday of the following week. The problem sets will be provided in the assignments section. No late homework will be accepted. You may discuss the problems with others in class, but you must (a) write up your eventual solution independently, and (b) list the names of students with whom you discussed the problem set. Problem sets may contain a MATLAB® component.

Grading

List of Topics

Calendar

The calendar below provides information on the course's lecture (L), recitations (R) and MATLAB® laboratory (M) sessions.