Intermediate Dynamics

This page contains links to set of notesexample problems, and exercises associated with a second course in rigid body dynamics. The notes cover topics relevant to two-dimensional and three-dimensional motion. A more complete presentation of three-dimensional, rigid body dynamics is provided in the 3D Dynamics eBook.

A set of exercises with answers  are provided at the bottom of this page. Two of the exercises recommend practice with MATLAB/Simulink/SimMechanics®.

Trademark: MATLAB, Simulink, and SimMechanics (now called Simscape Multibody) are all registered trademarks of The MathWorks, Inc. The MathWorks does not warrant the accuracy of the examples provided below.

ME555Homework01Figure03
Three Degree-of-Freedom Rotating Disk

References:

  1. L. Meirovitch, Methods of Analytical Dynamics, McGraw-Hill, 1970.
  2. T.R. Kane, P.W. Likins, and D.A. Levinson, Spacecraft Dynamics, McGraw-Hill, 1983
  3. T.R. Kane and D.A. Levinson, Dynamics: Theory and Application, McGraw-Hill, 1985
  4. R.L. Huston, Multibody Dynamics, Butterworth-Heinemann, 1990
  5. H. Baruh, Analytical Dynamics, McGraw-Hill, 1999
  6. H. Josephs and R.L. Huston, Dynamics of Mechanical Systems, CRC Press, 2002
  7. R.C. Hibbeler, Engineering Mechanics: Dynamics, 13th Ed., Pearson Prentice Hall, 2013
  8. J.L. Meriam and L.G. Craig, Engineering Mechanics: Dynamics, 3rd Ed, 1992
  9. F.P. Beer and E.R. Johnston, Jr. Vector Mechanics for Engineers: Dynamics, 4th Ed, 1984

Angular Motion and Angular Velocity

  1. Simple Angular Motion
  2. Summation Rule for Angular Velocities

Derivatives in Different Reference Frames

The Derivative Rule

Generalized Forces and the Principle of Virtual Work

  1. Generalized Forces
  2. Principle of Virtual Work
  3. Principle of Virtual Work – Example

Linearization of Equations of Motion, Natural Frequencies and Mode Shapes

  1. Linearization of Functions of One or Many Variables
  2. Natural Frequencies and Mode Shapes

Example Problems

  1. Example #1 – Angular Velocity and Angular Acceleration
  2. Example #2a – Calculation of Velocity using Direct Differentiation
    Example #2b – Calculation of Velocity using the Derivative Rule
  3. Example #3 – Calculation of Acceleration using the Derivative Rule
  4. Example #4 – Calculation of Velocity using the Two-Point Formula
  5. Example #5 – Calculation of Acceleration using the Two-Point Formula
  6. Example #6 – Calculation of Velocity and Acceleration using the Formulae for a Point Moving on a Body
  7. Example #7 – Calculation of Velocity using the Formula for a Point Moving on a Body
  8. Example #8 – Calculation of Acceleration using Formula for a Point Moving on a Body
  9. Example #9 – Calculation of Velocity using the Formula for a Point Moving on a Body
  10. Example #10 – Calculation of Acceleration using the Formula for a Point Moving on a Body
  11. Example #11 – Angular Momentum & Kinetic Energy of a Simple Crank Shaft
  12. Example #12 – Angular Momentum & Kinetic Energy of a Misaligned Disk
  13. Example #13 – Angular Momentum & Kinetic Energy of a Two DOF System
  14. Example #14 – Bearing Loads on a Simple Crank Shaft
  15. Example #15 – Bearing Loads on a Misaligned Disk
  16. Example #16 – Newton Equations of Motion for a Two DOF System
  17. Example #17 – Partial Velocities for a Slider-Crank Mechanism
  18. Example #18 – Principle of Virtual Work (Simple Mechanism)
  19. Example #19 – Principle of Virtual Work (Simple Mechanism)
  20. Example #20 – Lagrange’s Equations (1 DOF system)
  21. Example #21 – Lagrange’s Equations (2 DOF system)
  22. Example #22 – Lagrange’s Equations (2 DOF system)
  23. Example #23 – Lagrange’s Equations (3D, 2 DOF system)
  24. Example #24 – Linearization of Equations of Motion
  25. Example #25 – Linearization of Equations of Motion
  26. Example #26 – Natural Frequencies and Mode Shapes