Course Description

University of California, Davis
Department of Mechanical and Aerospace Engineering
Multibody Dynamics
Fall 2017, Lecture: TR 10:00-11:50 AM, Wickson Hall 1020
CRN: 62952 (MAE), 63548 (BIM)

After the completion of this class you will have developed the skills to model, interpret, simulate, and analyze multibody systems, i.e. systems which are made up of interconnected rigid bodies with arbitrary constraints and applied loads. Mathematical models of multibody systems are typically very useful at predicting the motion of macro scale objects. Newton's laws of motion are the foundation of developing predictive models of these systems. Examples of systems you will be able to model are: spacecraft trajectories, human/animal biomechanics, vehicle motion, robot motion, etc.

Catalog Description

Lecture—4 hours. Prerequisite: Engineering 102. Coupled rigid-body kinematics/dynamics; reference frames; vector differentiation; configuration and motion constraints; holonomicity; generalized speeds; partial velocities; mass; inertia tensor/theorems; angular momentum; generalized forces; comparing Newton/Euler, Lagrange's, Kane's methods; computer-aided equation derivation; orientation; Euler; Rodrigues parameters. (Same course as Biomedical Engineering 223.)—W, S. (W.) Eke, Ravani

Learning Objectives

Students will be able to:

  • formulate a model and free body diagram of multibody systems
  • incorporate holonomic and nonholonomic constraints into a multibody system
  • derive the nonlinear and linear equations of motion of a multibody system
  • simulate the motion of a multibody system with a computer
  • interpret and analyze the results of simulation
  • understand and explain notable dynamic phenomena


The only required prerequisite is ENG 102 or a similar course in introductory dynamics. You should also be proficient with at least one scientific programming language. We will be using Python in class.


Jason K. Moore
Assistant Professor of Teaching
2095 Bainer Hall

Time and Location

We will meet in Wickson 1020 on Tuesdays and Thursdays from 10:00 AM to 11:50 AM.

If you have any conflicts with the schedule you must tell me by email in the first week of class (major emergencies will be the only exception).

Office Hours

Office hours are Tuesdays and Wednesdays 1:10-2:00pm in Bainer 2095. If you can't make the regular scheduled office hours, check Jason's work calendar for an open time slot between 8:00 am and 6:30 pm Monday through Thursday and email him with a request for a meeting.

Academic Integrity

Academic dishonesty will not be tolerated. All assignments turned in for a grade must be your unique work and the exams should be completed solely by you with no assistance from others. Please visit the Academic Integrity web page from UC Davis Office of Student Judicial Affairs to review the campus' policy on academic responsibility and integrity and read the UC Davis code of academic conduct.

Course Text and Materials

The majority of preparation and readings for the lectures will come from this textbook:

Thomas R. Kane, and David A. Levinson. Dynamics, Theory and Application. McGraw Hill, 1985.

Note that the book is out of print, but you can download a PDF copy from Cornell's eCommons digital repository for personal use. Additionally, the following book may also be a useful reference for some topics:

Thomas R. Kane, Peter W. Likins, and David A. Levinson. Spacecraft Dynamics. McGraw Hill, 1983.

There are many advanced dynamics books that provide useful information but these two present the material in the context and notation that we will use in class. Other useful references will be added to the resources tab of this website as we move through the course.


We will be making extensive use of the computer aided algebra software SymPy and simulation software PyDy to model and simulate multibody systems. These packages are written in the open source Python programming language and leverage the SciPy ecosystem of scientific and engineering computing tools. You will have access to these through our JupyterHub server at You may also install the software on your own computer. It is recommended that bring your laptop, tablet, or phone to class to follow along with the interactive sessions (laptop is recommended). See the software page on this website for more information.

Assignments & Grades

Being a graduate class, I will not be focused on grading many different detailed aspects of the class. You will be expected to do as much or little practice as needed to pass the exams and complete your project. Homework problems will be suggested but not graded. I recommend talking through homework solutions with your classmates and the instructor during office hours.

Grades will be available in the grade book periodically throughout the course along with class statistics.

Assignment %
Exam 1 30%
Exam 2 30%
Project 40%
Two take home exams will be given. These must be completed individually. You can use any materials you want but you are on your honor to not discuss the exams questions with any other person other than the instructor.
You will be expected to complete a modeling, simulation, and analysis project that you design on your own. You are encouraged to discuss this project with others, but you must do all of the work and presentation yourself. You will give a short lightning presentation on the results to the class during the final exam time.


We will make use of Canvas for the course. Log in to with your Kerberos ID and passphrase then select MAE 223 001 FQ 2019.

We will be using several features in Canvas:

This will be my primary communication avenue to you. These announcements will be forwarded automatically to your UCD email address. You are expected to read these either through your email program or on the Canvas website.
Any assignments will be distributed here and collected here.
Your grades and basic stats on your relative performance will be available as the course goes along.
Copyrighted and private files, documents, and other resources will be available here for download. The rest will be available for download on this website.


Canvas Discussions
This is the first place to ask questions. Use this forum to ask questions that are general for the class. Try to restructure your less general questions into general ones so you can ask here. This minimizes the number of times a question has to be answered and allows both students and instructors to collectively answer questions.
Use email for individualized communication, i.e. for questions about project specifics or other personal needs. Prepend "[MAE223]" to their subject line.
Office Hours
Please come visit me in office hours to discuss your work. The earlier, the better and I recommend doing this often.
You may schedule an appointment with me outside of office hours if all of the above doesn't work for some reason. Use this as a last resort.