James W. Kamman, Ph.D.
Associate Professor Emeritus
Mechanical & Aerospace Engineering
Western Michigan University
Home Up Course Notes Homework/Tests SimMechanics eBook

An Introduction to Three-Dimensional, Rigid Body Dynamics

Below are links to a set of PDF files which together provide an introduction to three-dimensional, rigid body dynamics. The files are separated into two volumes. Volume I provides ten units of introduction to rigid body kinematics. The units of Volume II are currently being written and will provide an introduction to rigid body kinetics.

Much of the content presented in these files is also contained in PDF files accessible on the Course Notes pages for ME 5550 and ME 6590. The current files are built from and extend the notes presented on the Course Notes pages.

The contents of these files are free; however, many of the PDF files are password protected. The first three files have no password protection. The others are password protected. If you would like access to the password protected files, send an email request to me at: james.kamman@wmich.edu. The password is provided at no cost

The PDF files can be opened and read in any PDF viewer/reader application. In my experience, some of the viewers work better than others, so you may want to try different viewers to optimize your experience.

Volume I: Kinematics

Summary of Volume I Contents

  1. Unit 1 - Angular Velocity and Angular Acceleration - An Introduction

  2. Unit 2 - Velocity and Acceleration Using Direct Differentiation

  3. Unit 3 - Relative Kinematics of Two Points Fixed on a Rigid Body

  4. Unit 4 - Kinematics of a Point Moving on a Rigid Body

  5. Unit 5 - Rigid Body Orientation, Orientation Angles, and Angular Velocity

  6. Unit 6 - Rigid Body Orientation, Orientation Parameters, and Angular Velocity

  7. Unit 7 - Application of Concepts to Systems with Complex Interconnecting Joints

  8. Unit 8 - Introduction to Systems with Closed Kinematic Chains

  9. Unit 9 - Introduction to Systems with Rolling Constraints

  10. Unit 10 - Introduction to Modeling Mechanical System Kinematics Using MATLAB/Simulink/SimMechanics

Volume II: Kinetics

Summary of Volume II Contents

  1. Unit 1 - Inertia Matrices Angular Momentum Kinetic Energy

  2. Unit 2 - Newton/Euler Equations of Motion

  3. Unit 3 - Degrees of Freedom, Partial Velocities and Generalized Forces

  4. Unit 4 - Principal of Virtual Work and Lagrange's Equations 

  5. Unit 5 - D'Alembert's Principle and Kane's Equations  

  6. Unit 6 - Lagrange's Equations, D'Alembert's Principle, and Kane's Equations for Constrained Systems

  7. Unit 7 - Introduction to Modeling Mechanical System Kinetics Using MATLAB/Simulink/SimMechanics