An Introduction to Three-Dimensional, Rigid Body Dynamics

Below are links to a set of PDF files which together are an introduction to three-dimensional, rigid body dynamics. Currently, the files are separated into three volumes. Volumes I and II are an introduction to three-dimensional rigid body kinematics and dynamics. One unit in each of these volumes is an introduction to modeling in MATLAB/Simulink/SimScape Multibody®. A third volume is currently being written to provide an introduction to multibody kinematics.

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.

Trademarks: MATLAB, Simulink, and Simscape Multibody are all registered trademarks of The MathWorks, Inc. The MathWorks does not warrant the accuracy of the examples given in these notes.

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/Simscape Multibody 
11. Three-Dimensional Slider Crank Mechanism Movie:

Volume II: Kinetics

Summary of Volume II Contents  

1. Unit 1 – Inertia Matrices, Angular Momentum, and Kinetic Energy
2. Unit 2 – Newton/Euler Equations of Motion
3. Unit 3 – Degrees of Freedom, Partial Velocities and Generalized Forces
4. Unit 4 – Principle 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/Simscape Multibody  
8. Unit 8 – Basic Concepts of Linearization, Stability, Mode Shapes, and Natural Frequencies  
      YouTube – Veritasium – The Bizarre Behavior of Rotating Bodies
   

Volume III: Multibody Kinematics

Summary of Volume III Contents