Course Description

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.

Instructors

Time and Location

Lecture videos will be posted online for viewing each Friday, starting February 4, 2022. You will be expected to watch the videos before the work sessions on Tuesdays. Homework work sessions will occur each week on Tuesdays:

• Quarter 3: Tuesdays 13:45-15:45, 3mE-CZ D (James Watt) & Online via MS Teams
• Quarter 4: Tuesdays 15:45-17:45, 3mE-CZ D (James Watt) & Online via MS Teams

The current coronavirus regulations permit 75 students in the lecture hall at one time. If you want to attend in-person, you must sign up each week for one of the 75 slots on the appropriate group in Brightspace. All others will have to join via Microsoft Teams for these sessions. The MS Teams connection information is available in Brightspace.

Lecture topics are shown on the schedule page.

Academic Integrity

Academic dishonesty will not be tolerated. All homework assignments turned in for a grade must be your (or you and your partner's) unique work. You may base your answers off of external materials, but not your classmate's work. You will have to include a contribution explanation with each homework submission. This contribution explanation should explain the contributions each of the partner's made and any help you received from people other than the instructors.

If you make use of code found in other materials that you did not write yourself, either directly or in a modified form, you must follow the copyright licenses associated with that material. If there is no copyright license present, then you must obtain a written and signed permission from the author of the materials and provide that with your assignment submission. If there is a copyright license present in the materials you use (e.g. GPL, MIT, BSD, CC-BY), then you must follow the terms of that license. Most licenses, at minimum, require you to include the license with your work submission. This mirrors what you will have to do, by law, in your future work.

All code and written answers will be checked for plagiarism amongst student submissions and against external materials. Unattributed plagiarized materials will be marked with a 0 grade. Multiple offenses will result in no grade for the course.

Course Text and Materials

The course will be based primarily on these online lecture notes which will be provided incrementally as we proceed through the course:

Jason K. Moore. Learn Multibody Dynamics, 2020. https://moorepants.github.io/learn-multibody-dynamics

The primary principles and notation are based on this freely available book:

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, some topics will be derived from the following books:

Heike Vallery and Arend L. Schwab, "Advanced Dynamics", 3rd edition, Delft University of Technology, 2020, ISBN/EAN 978-90-8309-060-3

Thomas R. Kane, Peter W. Likins, and David A. Levinson. Spacecraft Dynamics. McGraw Hill, 1983. http://hdl.handle.net/1813/637.

Software

We will be making extensive use of the computer aided algebra software SymPy along with NumPy and SciPy to model and simulate multibody systems. These packages are written in the open source Python programming language and leverage the scientific Python ecosystem of scientific and engineering computing tools. You will have access to these through Vocareum in Brightspace. You may also install the software on your own computer. It is recommended that you bring your laptop to the work sessions. See the software page on this website for more information.

Assignments & Grades

Grade calculation statement updated on Feb, 11 2022.

The average of your best 10 of 12 homeworks will be counted for 60% of the course grade and the exam will count for 40% of the course grade. You must score at least a 3 of 10 (30%) on the exam to pass the course when the grade is in combination with your homework score. If the exam grade is better than the average homework grade or if you are taking a resit exam, then the course grade is 100% from the exam.

Homework

There will be 12 computational homework assignments. Homeworks will be made available via Brightspace-Vocareum one week before they are due. You may turn in homework as a pair or as an individual. To submit as a pair, you must invite your partner within the Vocareum interface for each homework. All homework submissions should be the unique work of the individual or the pair. You must provide a contribution statement for each homework explaining any help you have received and any copyright licenses for materials you have used. See the schedule page for homework deadlines.

Exam

The exam will have a 3 hour duration. You will be able to bring any physical printed resources available to you, e.g. books, Jupyter notebooks, websites. Effective use of the computational tools taught in class will give you the best chance at succeeding, but they are not necessarily required to succeed. No help from other people during the exam is permitted.

Exam Details

• The exam is Friday Jun 24 Exam 9:00-12:00 in Building: B66 Fellowship, Rooms: Studio Class Room 1 & 2.
• Register via Osiris.
• The exam will be in person at a computer lab on the TU Delft campus.
• The exam duration is 3 hours at the scheduled time.
• The exam will be on a computer with the Windows OS. You'll need your netid and password to log in.
• No internet access is permitted (computers have internet blocked). Leave your phones, tablets, computers, etc. in your bag.
• The exam questions will be delivered and answered using the Mobius software.
• Questions will be a combination of multiple choice, true/false, and numerical values.
• Jupyter Notebooks, Spyder, and Matlab are available for computation. SymPy, NumPy, SciPy, and matplotlib will be installed for Python. You will need numerical calculations for some problems.
• Numerical result questions will provide feedback if the answer is incorrect. Other questions will not.
• You will have unlimited tries for each question.
• You may bring any reference materials on paper.
• You may bring a single USB stick with reference materials. Make sure the drive is formatted with the NTFS file system. The computers have the following software:
  • Adobe Acrobat Reader for PDF files
  • Firefox for HTML files, images, etc.
  • Jupyter for ipynb files.
  • Spyder for .py files.
  • Notepad++ for text files.

Brightspace

We will be using several features in Brightspace:

Announcements

This will be the instructor's primary communication avenue to you. These announcements can be forwarded to your TU Delft email address. You are expected to read these when shared.

Content -> Vocareum (Jupyter Notebook Server)

You will access the homework Jupyter notebook assignments here. You can edit and execute the notebooks in the Vocareum interface that is linked via each assignment. The "Sandbox" assignment gives access to a Vocareum Jupyter instance where you can practice and explore the software.

Collaboration -> Discussions

All questions for the instructors (or fellow classmates) that are not of a private nature should be asked in Brightspace discussions. If you need to discuss something of a private nature with the instructor(s), use email.

Grades

Homework grades will be posted to Vocareum and/or Brightspace throughout the duration of the course.

Groups

To attend the work sessions in-person, you must sign up for that week's group. It is first come, first serve for the 75 open slots. As of February 18th, this is no longer required. See note above.