# Syllabus

## Course Description¶

University of California, Davis
Department of Mechanical and Aerospace Engineering
Multibody Dynamics
Fall 2017, Lecture: MW 10:00-11:50 AM
CRN: 63597

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
• derive the equations of motion of a multibody system
• incorporate holonomic and nonholonomic constraints into a multibody system
• simulate the motion of a multibody system with a computer
• interpret and analyze the results of simulation

### Prerequites¶

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

Jason K. Moore
2095 Bainer Hall
530-752-4805

## Time and Location¶

We will meet in Bainer 1070 on Mondays and Wednesday 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 (emergencies will be the only exception).

## Office Hours¶

Office hours are Tuesdays 1:10 pm to 2:00 pm and Thursdays 10:00 am to 10:50 am 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 dishonesty will not be tolerated. 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. http://hdl.handle.net/1813/638.

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. http://hdl.handle.net/1813/637.

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.

## Software¶

We will be making extensive use of PyDy and SymPy 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 bicycle.ucdavis.edu. You may also install the software on your own computer. You will need to bring your laptop, tablet, or phone to class to follow along with the interactive sessions. See the software page on this website for more information.

Being a graduate class, we 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 me during office hours.

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

Assignment %
Exam 1 30%
Exam 2 30%
Project 40%
Exams
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.
Project
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.

## Canvas¶

We will make use of Canvas for the course. Log in to canvas.ucdavis.edu with your Kerberos ID and passphrase then select MAE 223 001 FQ 2017.

We will be using several features in Canvas:

Announcements
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.
Assignments
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.
Files