The Dynamics Workbench

by Arthur Kuo

About the Dynamics Workbench

The Dynamics Workbench is a Mathematica package which can be used to analyze dynamics of arbitrary multibody systems. It is more flexible than many commercial packages, and is easier to use than many advanced packages. It is based on Kane's method, and offers three levels of use. At the introductory level, it allows one to assemble dynamic systems by connecting together rigid bodies using predefined joints. More advanced users can have access to functions which perform calculations such as partial velocities or angular momentum, and can define their own joints. At the most advanced level, users can use the Dynamics Workbench as a dynamics calculator, which performs vector arithmetic and calculus on multiple reference frames.
Update: 3.6 The Dynamics Workbench has been updated to remove a name conflict with Mathematica 5.0.
Update: 3.7 Fixed a change in Mathematica's dot product, which caused in slow dot products for large systems.

Example: Analysis of a pendulum

This is a brief example of an analysis of a pendulum, done with the Dynamics Workbench. It is available as a Mathematica notebook, and as a PDF document. Note that the notebook is a text document and can be read on any platform that runs Mathematica, but some pictures may not display properly (the pictures were generated on a Macintosh). If this is the case, the pictures can be viewed from the PDF document.

Pendulum.nb: [Notebook] [PDF]

Example: Ballistic walking plus tutorial

This is an example of a slightly more advanced system, in which a nonlinear system is simulated. The system models ballistic motion of the swing leg during human locomotion, form Mochon & McMahon's 1985 paper in Journal of Biomechanics. This document also contains a tutorial and a short description of commands for the Dynamics Workbench. As in the example above, the notebook is a text document, with embedded pictures which may not display properly. Use the PDF document if this is the case on your system.

Ballistic walking example & tutorial DW_Tutorial.nb: [Notebook] [PDF]

The Dynamics Workbench Package v3.7

The Dynamics Workbench is copyrighted but may be copied without charge. It is a Mathematica package in text format, and should be compatible with any platform which can run Mathematica. Documentation for the Dynamics Workbench is work in progress. Please e-mail feedback to

DynamicsWorkbench.m: [Package]

If you don't own a copy of Mathematica, you can download MathReader, which is a free viewer for Mathematica documents.

You may also need Adobe Acrobat to read PDF files.