Dynamics and Control I

Dynamics and Control I

Multiple frames of reference help explain the position, velocity and acceleration of a spider on a spinning frisbee. See the video for lecture 2 and the reading on kinematics for more on this introductory problem. (Frisbee photo courtesy of Crys Mascarenas; spider photo courtesy of B. Smith. Collage by MIT OpenCourseWare.)

Course Description

This class is an introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Topics include kinematics; force-momentum formulation for systems of particles and rigid bodies in planar motion; work-energy concepts; virtual displacements and virtual work; Lagrange's equations for systems of particles and rigid bodies in planar motion; linearization of equations of motion; linear stability analysis of mechanical systems; free and forced vibration of linear multi-degree of freedom models of mechanical systems; and matrix eigenvalue problems. The class includes an introduction to numerical methods and using MATLAB® to solve dynamics and vibrations problems.

This version of the class stresses kinematics and builds around a strict but powerful approach to kinematic formulation which is different from the approach presented in Spring 2007. Our notation was adapted from that of Professor Kane of Stanford University.

Download Course Materials

2-003JFall-2007.zip (ZIP - 4.82 MB)

Click the link above to start downloading this course.

Video Lectures

Special software is required to use some of the files in this section: .rm.

This page presents videos for the first half of the class lectures. These lectures are particularly important because they contain the new kinematics approach.

Note: video is not available for Lecture 6.

Disclaimer from Professor Sarma: A lecture is like a live performance – there are no retakes. So when you watch these videos, please keep in mind that I am human, and I make mistakes. For example, at minute 12 of the video of Lec #2 I make a mistake when I describe why the earth is an approximate inertial frame. What I mean to say is that the Earth, though moving, is accelerating relatively slowly with respect to some imaginary but real inertial frame when compared with, say a space-craft. So we treat it as an inertial frame, and experiments show that that is a good approximation. That's not how I say it in the video, but the students did understand what I meant because the staff of the class interact with the students in a number of ways. So watch these videos but stay alert – and keep in mind that besides making mistakes, I also sometimes joke with my students.

LEC #	TOPICS	VIDEOS
1	Course information Begin kinematics: frames of reference and frame notation	(RM - 56K) (RM - 220K)
2	The "spider on a Frisbee" problem Kinematics using first principles: "downconvert" to ground frame	(RM - 56K) (RM - 220K)
3	Pulley problem, angular velocity, magic formula	(RM - 56K) (RM - 220K)
4	Magic and super-magic formulae	(RM - 56K) (RM - 220K)
5	Super-magic formula, degrees of freedom, non-standard coordinates, kinematic constraints	(RM - 56K) (RM - 220K)
6	Single particle: momentum, Newton's laws, work-energy principle, collisions
7	Impulse, skier separation problem	(RM - 56K) (RM - 220K)
8	Single particle: angular momentum, example problem Two particles: dumbbell problem, torque	(RM - 56K) (RM - 220K)
9	Dumbbell problem, multiple particle systems, rigid bodies, derivation of torque = I*alpha	(RM - 56K) (RM - 220K)
10	Three cases, rolling disc problem	(RM - 56K) (RM - 220K)