everything.study
1.053

Dynamics and Control I

4-1-7 units. REST · Undergraduate

See description under subject 2.003[J] .

Fall 2011 · Engineering Dynamics

This course is an introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Topics covered include kinematics, force-momentum formulation for systems of particles and rigid bodies in planar motion, work-energy concepts, virtual displacements and virtual work. Students will also become familiar with the following topics: Lagrange's equations for systems of particles and rigid bodies in planar motion, and linearization of equations of motion. After this course, students will be able to evaluate free and forced vibration of linear multi-degree of freedom models of mechanical systems and matrix eigenvalue problems.

Readings

  • [Hibbeler]= Hibbeler, Russell C. Engineering Mechanics: Dynamics . 12th ed. Prentice Hall, 2009. ISBN: 9780136077916.
    Listed reading
  • [Williams]= Williams, J. Fundamentals of Applied Dynamics . John Wiley & Sons, 1995. ISBN: 9780471109372.
    Listed reading
Fall 2007

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.

Readings

  • The cited chapter/section numbers are in the course textbook:
    Listed reading
  • Williams, J. H., Jr. Fundamentals of Applied Dynamics . New York, NY: John Wiley and Sons, Inc., 2006. ISBN: 9780470133859.
    Listed reading
  • SES #: 4 · TOPICS: Magic and super-magic formulae · READINGS: 3.4, 3.5 theory
    Reading assignment
  • SES #: 5 · TOPICS: Super-magic formula, degrees of freedom, non-standard coordinates, kinematic constraints · READINGS: 3.5 problems, 3.6
    Reading assignment
  • SES #: 6 · TOPICS: Single particle: momentum, Newton’s laws, work-energy principle, collisions · READINGS: 4.1, 4.2
    Reading assignment
  • SES #: 9 · TOPICS: Dumbbell problem, multiple particle systems, rigid bodies, derivation of torque = I*alpha · READINGS: 6.2
    Reading assignment
  • SES #: 10 · TOPICS: Three cases, rolling disc problem · READINGS: 6-3.1, 6-3.2 (restrict to 2D, most of the material is 3D)
    Reading assignment
  • SES #: 14 · TOPICS: Generalized coordinates, introduction to Lagrangian, example problem · READINGS: 5-4.1, 5-5 (see equations alone), examples in 5-5 without generalized force calculations
    Reading assignment
  • SES #: 15 · TOPICS: Lagrangian derivation · READINGS: 5-4.3, 5-4.4
    Reading assignment
  • SES #: 16 · TOPICS: Generalized forces, double pendulum problem · READINGS: 5-4.4, examples in 5-5, 6-5, 2D examples in 6-6
    Reading assignment
  • SES #: 17 · TOPICS: Example problem · READINGS: Examples in 5-5, 6-5, 2D examples in 6-6
    Reading assignment
  • SES #: 21 · TOPICS: Single DOF system: equilibrium, linearization, stability analysis · READINGS: 8-1, 8-3 introduction
    Reading assignment
  • SES #: 22 · TOPICS: Free response of a damped oscillator · READINGS: 8-3.1
    Reading assignment
  • SES #: 23 · TOPICS: Free response (cont.) · READINGS: 8-3.1
    Reading assignment
  • Williams, J. H., Jr. Fundamentals of Applied Dynamics . New York, NY: John Wiley and Sons, Inc., 2006. ISBN: 9780470133859.
    Required
  • Meriam, J. L., and L. G. Kraige. Engineering Mechanics: Dynamics . 5th ed. Vol. 2. New York, NY: J. Wiley & Sons, 2001. ISBN: 9780471406457.
    Recommended
Spring 2007

Introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. 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; matrix eigenvalue problems. Introduction to numerical methods and MATLAB® to solve dynamics and vibrations problems.

Readings

  • Williams, J. H., Jr. Fundamentals of Applied Dynamics . New York, NY: John Wiley and Sons, Inc., 2006. ISBN: 9780470133859. (Williams)
    Required
  • Bedford, A., and Wallace L. Fowler. Engineering Mechanics: Dynamics . 2nd ed. Menlo Park, CA: Addison-Wesley Publishing, Inc., 1998. ISBN: 9780201180718. (Bedford and Fowler)
    Recommended
  • The readings consist of selected chapters from Williams and the lecture notes . ↗
    Recommended
  • Chapters 1 and 2
    Recommended
  • Williams, J. H., Jr. Fundamentals of Applied Dynamics . New York, NY: John Wiley and Sons, Inc., 2006. ISBN: 9780470133859.
    Required
  • Bedford, A., and Wallace L. Fowler. Engineering Mechanics: Dynamics . 2nd ed. Menlo Park, CA: Addison-Wesley Publishing, Inc., 1998. ISBN: 9780201180718.
    Recommended
Fall 2002 · Dynamics and Vibration (13.013J)

Topics

  • Kinematics
  • Recitation
  • Momentum Formulation for Systems of Particles
  • Variational Formulation for Systems of Particles
  • Dynamics of Systems Containing Rigid Bodies
  • Vibration of Linear Lumped-Parameter Systems
  • Dynamics of Continuous Systems

Readings

  • Williams, James H., Jr. Fundamentals of Applied Dynamics . John Wiley & Sons, Inc., 1996.
    Required
  • Rao, S. S. Mechanical Vibrations . 3rd ed. Addison Wesley, 1995.
    Listed reading
  • Beer, Ferdinand Pierre. Vector Mechanics for Engineers . McGraw-Hill, 1988.
    Listed reading

Prerequisites & course information

Same subject as 2.003[J] Prereq: Physics II (GIR) ; Coreq: 2.087 or 18.03 U (Fall, Spring) 4-1-7 units. REST

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