everything.study
2.032

Dynamics

4-0-8 units · Graduate

Review of momentum principles. Hamilton's principle and Lagrange's equations. Three-dimensional kinematics and dynamics of rigid bodies. Study of steady motions and small deviations therefrom, gyroscopic effects, causes of instability. Free and forced vibrations of lumped-parameter and continuous systems. Nonlinear oscillations and the phase plane. Nonholonomic systems. Introduction to wave propagation in continuous systems.

Fall 2004

Topics

  • Examples of Single Particle Dynamics
  • Examples of Single Particle Dynamics (cont.)
  • Dynamics of Systems of Particles: Linear and Angular Momentum Principles, Work-energy Principle
  • Linear and Angular Momentum Principle for Rigid Bodies
  • Work-energy Principle for Rigid Bodies
  • Examples for Lecture 8 Topics
  • Examples for Lecture 9 Topics
  • Generalized Coordinates, Constraints, Virtual Displacements
  • Generalized Coordinates, Constraints, Virtual Displacements (cont.)
  • Examples for Lecture 17 Topics
  • Lagrange Multipliers, Determining Holonomic Constraint Forces, Lagrange’s Equation for Nonholonomic Systems, Examples
  • Linearized Equations of Motion Near Equilibria of Holonomic Systems
  • Damped and Forced Vibrations Near Equilibria

Readings

  • The course will be based on the material presented in the lectures. There is no required textbook, although the following books are recommended.
    Listed reading
  • Baruh, H. Analytical Dynamics . New York, NY: McGraw-Hill, 1998. ISBN: 9780073659770.
    Listed reading
  • Ginsberg, J. H. Advanced Engineering Dynamics. 2nd ed. Cambridge, UK: Cambridge University Press, 1995. ISBN: 9780521470216.
    Listed reading
  • Crandall, S. H., D. C. Karnopp, E. F. Kurtz, Jr., and D. C. Pridmore-Brown. Dynamics of Mechanical and Electromechanical Systems . Malabar, FL: Krieger, 1982. ISBN: 9780898745290.
    Listed reading
  • Moon, F. C. Applied Dynamics . New York, NY: Wiley, 1998. ISBN: 9780471138280.
    Listed reading
  • Greenwood, D. T. Classical Dynamics . New York, NY: Dover Publications, 1997. ISBN: 9780486696904.
    Listed reading
  • ———. Principles of Dynamics . Upper Saddle River, NJ: Prentice-Hall, 1987. ISBN: 9780137099818.
    Listed reading
  • The following table lists sample readings, by lecture session, from Baruh’s Analytical Dynamics .
    Listed reading
  • LEC #: 4 · TOPICS: Dynamics of Systems of Particles: Linear and Angular Momentum Principles, Work-energy Principle · READINGS: 3.1-3.4
    Reading assignment
  • LEC #: 8 · TOPICS: Linear and Angular Momentum Principle for Rigid Bodies · READINGS: 8.1, 8.2
    Reading assignment
  • LEC #: 9 · TOPICS: Work-energy Principle for Rigid Bodies · READINGS: 8.9
    Reading assignment
  • LEC #: 13 · TOPICS: Generalized Coordinates, Constraints, Virtual Displacements · READINGS: 4.1-4.4
    Reading assignment
  • LEC #: 20 · TOPICS: Lagrange Multipliers, Determining Holonomic Constraint Forces, Lagrange’s Equation for Nonholonomic Systems, Examples · READINGS: 4.10
    Reading assignment
  • LEC #: 22 · TOPICS: Linearized Equations of Motion Near Equilibria of Holonomic Systems · READINGS: 5.3
    Reading assignment
  • LEC #: 25 · TOPICS: Damped and Forced Vibrations Near Equilibria · READINGS: 5.7
    Reading assignment
  • Goldstein, H. Classical Mechanics. Cambridge, MA: Addison-Wesley, 1959.
    Listed reading
  • Hartog, J. P. Den. Mechanics . New York: Dover, 1961.
    Listed reading
  • Marion, J. B. Classical Dynamics of Particles and Systems. 2nd ed. New York: Academic Press, 1970.
    Listed reading
  • Landau, L. D., and E. M. Lifshitz. Mechanics. 3rd ed. New York: Pergamon, 1976.
    Listed reading
  • Williams, J. H., Jr. Fundamentals of Applied Dynamics. New York: John Wiley, 1996.
    Listed reading
  • Hartog, J. P. Den. Mechanical Vibrations. New York: McGraw-Hill, 1956.
    Listed reading
  • Meirovitch, L. Elements of Vibration Analysis. New York: McGraw-Hill, 1975.
    Listed reading
  • ———. Analytical Methods in Vibrations. New York: Macmillan, 1967.
    Listed reading
  • Pippard, A. B. Response and Stability. New York: Cambridge University Press, 1985.
    Listed reading
  • Nayfeh, A. H., and D.T. Mook. Nonlinear Oscillations. New York: Wiley-Interscience, 1979.
    Listed reading
  • Strogatz, S. H. Nonlinear Dynamics and Chaos. Reading, MA: Addison-Wesley, 1994.
    Listed reading
  • The course will be based on the material presented in the lectures. There is no required textbook, although the following books are recommended and will be placed on library reserve.
    Listed reading

Prerequisites & course information

Prereq: 2.003[J] G (Fall) 4-0-8 units

Sources