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Dynamics and Control I >> Content Detail



Syllabus



Syllabus

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A list of topics by session is available in the calendar below.



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


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



Recommended Texts


Amazon logo 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



ACTIVITIESPERCENTAGES
Homework (including MATLAB® problems)30%
Mid-term exams (2)40%
Final exam30%



Recommended Citation


For any use or distribution of these materials, please cite as follows:

Thomas Peacock, Nicolas Hadjiconstantinou, Sanjay Sarma, and Peter So, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].



List of Topics



SES #Topics
I. Motion of a Single Particle
L1-L3

Kinematics: Trajectory, Velocity, Acceleration, Inertial Frame, Moving Frames

Forces and Torques

Linear Momentum Principle

Angular Momentum Principle

Work-Energy Principle

Equations of Motion

II. Motion of Systems of Particles
L4-L6

Internal and External Forces

Linear Momentum Principle

Angular Momentum Principle

Work-Energy Principle

Conservative Systems

Impulsive Forces

Collisions

III. 2D Motion of Rigid Bodies
L7-L12

Kinematics: Angular Velocity, Instantaneous Center of Rotation

Linear Momentum Principle

Angular Momentum Principle

Work-Energy Principle

Parallel Axis Theorem

IV. Introduction to Lagrangian Dynamics
L13-L19

Constraints and Forces

Ideal Constraints

Virtual Displacements

Virtual Work

D'Alembert's Principle

Generalized Coordinates and Forces

Lagrangian Equations of Motion For 2D Holonomic Systems of Particles

Equilibria

Linearization of Equations

Stability

V. Vibrations
L20-L24

1-Degree-of-Freedom Oscillations: Natural Frequencies, Free-, Damped-, and Forced Response

Multi-Degree-of-Freedom Oscillations: Natural Frequencies, Normal Modes, Free-, Damped-, and Forced Response

Time Response

Frequency Response

Bode Plots




Calendar


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


ses #TOPICSKEY DATES
I. Motion of a Single Particle
L1Newton's Laws, Cartesian and Polar Coordinates, Dynamics of a Single Particle
M1Introduction and Overview of MATLAB®
L2Work-Energy PrincipleProblem set 1 out
L3Dynamics of a Single Particle: Angular Momentum
R1Kinematics
M2Lab 1: MATLAB® Interface and Matrix Multiplication
II. Motion of Systems of Particles
L4Systems of Particles: Angular Momentum and Work Energy Principle

Problem set 1 due

Problem set 2 out

L5Systems of Particles: Example 1: Linear Momentum and Conservation of Energy, Example 2: Angular Momentum
R2Systems of Particles: Linear and Angular Momentum, Solutions in MATLAB®
M3Lab 2: Conditionals I
L6Collisions

Problem set 2 due

Problem set 3 out

III. 2D-Motion of Rigid Bodies
L72D-Motion of Rigid Bodies: Kinematics
R3Collisions and Problem Set 3 Hints
M4Lab 3: Conditionals II
L82D-Motion of Rigid Bodies: Kinematics - Instant Centers; Kinetics

Problem set 3 due

Problem set 4 out

L92D-Motion of Rigid Bodies: Kinetics, Parallel Axis Theorem
R4Instant Centers and Problem Set 4 Hints
M5Lab 4: Functions I
L102D-Motion of Rigid Bodies: Falling Stick Example, Work-Energy Principle

Problem set 4 due

Problem set 5 out

L112D-Motion of Rigid Bodies: Finding Moments of Inertia, Rolling Cylinder with Hole Example
R5Moments of Inertia and Problem Set 5 Hints
M6Lab 5: Functions II
L122D-Motion of Rigid Bodies: Rolling Cylinder and Rocker Examples

Problem set 5 due

Exam 1 two days after Ses #L12

R6Exam 1: Problems 1 and 2
M7Lab 6: Algorithms
M8Lab 7: ODE I
IV. Introduction to Lagrangian Dynamics
L13Lagrangian Dynamics: Generalized Coordinates and Forces
L14Lagrangian Dynamics: Virtual Work and Generalized Forces
R7Virtual Work, Generalized Forces, Problem Set 6 Hints
M9Lab 8: ODE II
L15Lagrangian Dynamics: Derivations of Lagrange's Equations and Examples

Problem set 6 due

Problem set 7 out

L16Lagrangian Dynamics: Examples
R8Problem Set 7 Hints
M10Lab 9: Eigenvalue Problems
L17Lagrangian Dynamics: Examples and Equilibrium Analysis

Problem set 7 due

Problem set 8 out

R9Problem Set 8 Hints: Problem 1
M11Lab 10: Project
L18Lagrangian Dynamics: Examples and Equilibrium Analysis
L19Lagrangian Dynamics: Examples and Equilibrium Analysis

Problem set 8 due

Exam 2 five days after Ses #L19

R10Rolling Disk: Sample Exam Question
M12Lab 11: Project
V. Vibrations
L20Vibrations: Second Order Systems with One Degree of Freedom - Free ResponseProblem set 9 out
R11Review of Lecture 20: Second Order Systems with One Degree of Freedom
M13Lab 12: Project
L21Vibrations: Second Order Systems with One Degree of Freedom - Forced Response
L22Vibrations: Free Response of Multi-Degree-of-Freedom Systems

Problem set 9 due

Problem set 10 out (optional)

R12Problem Set 10 Hints: Problem 3
M14Lab 13: Project
L23Vibrations: Two Degrees of Freedom Systems - Wilberforce Pendulum
L24Vibrations: Forced Response of Multi-Degree-of-Freedom SystemsFinal exam 8 days after Ses #L24

 








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