James W. Kamman, Ph.D.
Associate Professor Emeritus
Mechanical & Aerospace Engineering
Western Michigan University
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ME 6590 Multibody Dynamics: Selected Course Notes

Below are links to some selected course notes.  Each is in PDF format that you can read and print using Adobe Acrobat Reader.  To download a free copy of Acrobat reader, click on the Acrobat Reader link below.

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Selected Course Notes: 

  1. Representation of Vector Operations as Matrix Operations

  2. Coordinate Transformation Matrices

  3. Orientation Angles of a Rigid Body in Three Dimensions

  4. Angular Velocity and Orientation Angles

  5. Maple: Transformation Matrix for a 1-2-3 Body-Fixed Rotation Sequence

  6. Maple: Orientation Angle Derivatives and Angular Velocity Components

  7. Orientation of a Rigid Body Using Euler Parameters

  8. Time Derivative of the (Coordinate) Transformation Matrices

  9. Euler Parameters and Angular Velocity Components

  10. Maple: Euler Parameters and Angular Velocity Components

  11. Conversion of Direction Cosines to Euler Parameters

  12. Conversion of Direction Cosines to 1-2-3 Body-Fixed Angle Sequence

  13. Maple: Conversion of Direction Cosines to 1-2-3 Angle Sequence

  14. Generalized Coordinates, Quasi-Coordinates, and Generalized Speeds

  15. Angular Velocity & Partial Angular Velocity Using Absolute Coordinates

  16. Coordinate Transformation Matrices Using Relative Coordinates

  17. Angular Velocity & Partial Angular Velocity Using Relative Coordinates

  18. Angular Acceleration Using Absolute Coordinates

  19. Angular Acceleration Using Relative Coordinates

  20. Velocities and Partial Velocities Using Absolute Coordinates

  21. Velocities and Partial Velocities Using Relative Coordinates

  22. Accelerations Using Absolute Coordinates

  23. Accelerations Using Relative Coordinates

  24. Body-Connection Array

  25. Connecting Joints - Part I

  26. Connecting Joints - Part II

  27. Matrices and Second Order Dyadics

  28. Moments and Products of Inertia and the Inertia Matrix

  29. Principal Moments of Inertia and Principal Directions

  30. Maple: Example 6.7 on page 345 of text (Baruh, 1999)

  31. Maple: Symbolic Evaluation of Characteristic Equation of Inertia Matrix

  32. Constraints for Multibody Systems

  33. Lagrange's Equations for MDOF Systems with Constraints

  34. Constraint Relaxation Method: Meaning of Lagrange Multipliers

  35. Simulink Models of a Simple Pendulum

  36. D'Alembert's Principle for MDOF Systems

  37. Examples for D'Alembert's Principle

  38. Generalized Speeds, Partial Angular Velocities, and Partial Velocities

  39. Kane's Equations for MDOF Systems

  40. Examples for Kane's Equations

  41. Equations of Motion for a Multibody System

  42. Multibody Equations of Motion - Example

  43. Constrained Multibody Systems with Energy Theorem