**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 an introduction to rigid body kinematics. The units of Volume II provide an introduction to rigid body kinetics. One unit in each volume provides an introduction to modeling in MATLAB/Simulink/SimMechanics® (SimMechanics is now called SimScape Multibody).

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 SimMechanics (now called 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

- Unit 1 – Angular Velocity and Angular Acceleration – An Introduction
- Unit 2 – Velocity and Acceleration using Direct Differentiation
- Unit 3 – Relative Kinematics of Two Points Fixed on a Rigid Body
- Unit 4 – Kinematics of a Point Moving on a Rigid Body
- Unit 5 – Rigid Body Orientation, Orientation Angles, and Angular Velocity
- Unit 6 – Rigid Body Orientation, Orientation Parameters, and Angular Velocity
- Unit 7 – Application of Concepts to Systems with Complex Interconnecting Joints
- Unit 8 – Introduction to Systems with Closed Kinematic Chains
- Unit 9 – Introduction to Systems with Rolling Constraints
- Unit 10 – Introduction to Modeling Mechanical System Kinematics Using MATLAB/Simulink/SimMechanics

**Volume II: Kinetics**

## Summary of Volume II Contents

- Unit 1 – Inertia Matrices, Angular Momentum, and Kinetic Energy
- Unit 2 – Newton/Euler Equations of Motion
- Unit 3 – Degrees of Freedom, Partial Velocities and Generalized Forces
- Unit 4 – Principle of Virtual Work and Lagrange’s Equations
- Unit 5 – d’Alembert’s Principle and Kane’s Equations
- Unit 6 – Lagrange’s Equations, d’Alembert’s Principle, and Kane’s Equations for Constrained Systems
- Unit 7 – Introduction to Modeling Mechanical System Kinetics Using MATLAB/Simulink/SimMechanics
- Unit 8 – Basic Concepts of Linearization, Stability, Mode Shapes, and Natural Frequencies (updated 1/7/2022)

YouTube – Veritasium – The Bizarre Behavior of Rotating Bodies