# Dynamics and Control I

- Institution: Massachusetts Institute of Technology
- Department: Mechanical Engineering; Civil and Environmental Engineering
- Taught by: Prof. Nicholas Makris, Prof. Peter So, Prof. Sanjay Sarma, Dr. Yahya Modarres-Sadeghi
- Term: Fall 2007
- Level: Undergraduate
- Language: English
- Subjects: Mathematics, Engineering, Earth and environment
- Source: [MIT OpenCourseWare](https://ocw.mit.edu/courses/2-003j-dynamics-and-control-i-fall-2007/)
- Licence: [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/) (Non-commercial use only.)
- Syllabus: [at the source](https://ocw.mit.edu/courses/2-003j-dynamics-and-control-i-fall-2007/pages/syllabus/)
- Readings: [at the source](https://ocw.mit.edu/courses/2-003j-dynamics-and-control-i-fall-2007/pages/readings/)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

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.

## Lectures

1. [Lecture 1: Course information; Begin kinematics](https://invisiblenetwork.ai/learn/mit/2-003j-dynamics-and-control-i-fall-2007/de762f427680), 42 min (Video)
2. [Lecture 2: The "spider on a Frisbee" problem](https://invisiblenetwork.ai/learn/mit/2-003j-dynamics-and-control-i-fall-2007/4a263600adf6), 1 h 18 min (Video)
3. [Lecture 3: Pulley problem, angular velocity, magic formula](https://invisiblenetwork.ai/learn/mit/2-003j-dynamics-and-control-i-fall-2007/f7162f0dbfe7), 1 h 20 min (Video)
4. [Lecture 4: Magic and super-magic formulae](https://invisiblenetwork.ai/learn/mit/2-003j-dynamics-and-control-i-fall-2007/4810814eaf58), 1 h 19 min (Video)
5. [Lecture 5: Super-magic formula, degrees of freedom, non-standard coordinates, kinematic constraints](https://invisiblenetwork.ai/learn/mit/2-003j-dynamics-and-control-i-fall-2007/882f9cdbafea), 1 h 20 min (Video)
6. [Lecture 7: Impulse, skier separation problem](https://invisiblenetwork.ai/learn/mit/2-003j-dynamics-and-control-i-fall-2007/722bdf1ad038), 1 h 17 min (Video)
7. [Lecture 8: Single particle; Two particles](https://invisiblenetwork.ai/learn/mit/2-003j-dynamics-and-control-i-fall-2007/caf24a697c7b), 1 h 18 min (Video)
8. [Lecture 9: Dumbbell problem, multiple particle systems, rigid bodies, derivation of torque](https://invisiblenetwork.ai/learn/mit/2-003j-dynamics-and-control-i-fall-2007/60f94f0f30eb), 1 h 21 min (Video)
9. [Lecture 10: Three cases, rolling disc problem](https://invisiblenetwork.ai/learn/mit/2-003j-dynamics-and-control-i-fall-2007/606010633564), 1 h 14 min (Video)