This course develops student’s ability to accurately model the dynamics of single and multi-body engineering systems undergoing motion in 3D space. The course begins with formulating the differential geometry and kinematics of curvilinear coordinates to permit kinematic descriptions of relative motion and rotation of rigid bodies and mechanisms subject to common engineering constraints such as substructure interconnections, dry friction, and rolling. Momentum and inertia properties of rigid body dynamics follow. Students are then introduced to analytical dynamics, where Lagrange’s equations and Kane’s method are derived and studied to facilitate efficient formulation of the equations of motion governing the dynamics of systems subject to conservative and non-conservative forces and engineering constraints. The course also concludes with gyroscopic dynamics with applications to inertial guidance and spacecraft attitude dynamics. Prerequisite(s): Mathematics through calculus and linear algebra.
The course materials are divided into modules which can be accessed by clicking Course Modules on the left menu. A module will have several sections including the overview, content, readings, discussions, and assignments. You are encouraged to preview all sections of the module before starting. Most modules run for a period of seven (7) days, exceptions are noted in the Course Outline. You should regularly check the Announcements for any change/update on assignment due dates.
The goal of this course is to enable students to accurately model non-trivial engineering systems. That is, describing the kinematics and dynamics of systems subject to constraints and/or undergoing motion described better by curvilinear coordinates. Students are also introduced to the field of analytical dynamics to enable efficient modeling of engineering systems sing results from the Calculus of Variations and the Principles of Virtual Work and Least Action.
You will need access to a recent version of MATLAB. The MATLAB Total Academic Headcount (TAH) license is now in effect. This license is provided at no cost to you. Send an email to firstname.lastname@example.org to request your license file/code. Please indicate that you need a standalone file/code. You will need to provide your first and last name, as well as your Hopkins email address. You will receive an email from Mathworks with instructions to create a Mathworks account. The MATLAB software will be available for download from the Mathworks site.
Optionally, you will need access to a recent version of MATHEMATICA. The MATHEMATICA Total Academic Headcount (TAH) license is now in effect. This license is provided at no cost to you. You can go to log in to http://my.jhu.edu. Then click on “Technology”, and then go to “mySoftware” and search for MATHEMATICA.
It is expected that each module will take approximately 7-10 hours per week to complete. Here is an approximate breakdown: reading the assigned sections of the texts as well as some outside reading (approximately 2-3 hours per week), listening to the audio annotated slide presentations (approximately 1–2 hours per week), and working problems in assignments (approximately 4-5 hours per week).
This course will consist of the following basic student requirements:
Preparation and Participation (5% of Final Grade Calculation)
You are responsible for carefully reading all assigned material and being prepared for discussion. The majority of readings are from the course text. Additional reading may be assigned to supplement text readings.
Post your initial response to the discussion questions by the evening of day 3 for that module week. Posting a response to the discussion question is part one of your grade for module discussions (i.e., Timeliness).
Part two of your grade for module discussion is your interaction (i.e., responding to classmate postings with thoughtful responses) with at least two classmates (i.e., Critical Thinking). Just posting your response to a discussion question is not sufficient; we want you to interact with your classmates. Be detailed in your postings and in your responses to your classmates' postings. Feel free to agree or disagree with your classmates. Please ensure that your postings are civil and constructive.
I will monitor module discussions and will respond to some of the discussions as discussions are posted. In some instances, I/we will summarize the overall discussions and post the summary for the module.
Evaluation of preparation and participation is based on contribution to discussions.
Preparation and participation is evaluated by the following grading elements:
Preparation and participation is graded as follows:
Assignments (65% of Final Grade Calculation)
Assignments will include a mix of qualitative assignments (e.g. literature reviews, model summaries), quantitative problem sets, and case study updates. Include a cover sheet with your name and assignment identifier. Also include your name and a page number indicator (i.e., page x of y) on each page of your submissions. Each problem should have the problem statement, assumptions, computations, and conclusions/discussion delineated. All Figures and Tables should be captioned and labeled appropriately.
All assignments are due according to the dates in the Calendar.
Late submissions will be reduced by one letter grade for each week late (no exceptions without prior coordination with the instructors).
If, after submitting a written assignment you are not satisfied with the grade received, you are encouraged to redo the assignment and resubmit it. If the resubmission results in a better grade, that grade will be substituted for the previous grade.
Qualitative assignments are evaluated by the following grading elements:
Qualitative assignments are graded as follows:
Quantitative assignments are evaluated by the following grading elements:
Quantitative assignments are graded as follows:
Exams (30% of Final Grade Calculation, combined from 15% for Midterm and 15% for Final)
Students may use the course texts to complete the exams.
The exams are evaluated by the following grading elements:
Exams are graded as follows:
Assignments are due according to the dates posted in your Canvas course site. You may check these due dates in the Course Calendar or the Assignments in the corresponding modules. I will post grades one week after assignment due dates.
We generally do not directly grade spelling and grammar. However, egregious violations of the rules of the English language will be noted without comment. Consistently poor performance in either spelling or grammar is taken as an indication of poor written communication ability that may detract from your grade.
A grade of A indicates achievement of consistent excellence and distinction throughout the course—that is, conspicuous excellence in all aspects of assignments and discussion in every week.
A grade of B indicates work that meets all course requirements on a level appropriate for graduate academic work. These criteria apply to both undergraduates and graduate students taking the course.
EP uses a +/- grading system (see “Grading System”, Graduate Programs catalog, p. 10).
100-98 = A+
97-94 = A
93-90 = A−
89-87 = B+
86-83 = B
82-80 = B−
79-77 = C+
76-73 = C
72-70 = C−
69-67 = D+
66-63 = D
<63 = F
Final grades will be determined by the following weighting:
% of Grade
Preparation and Participation
Exams (Midterm + Final)
30% (15% + 15%)
Deadlines for Adding, Dropping and Withdrawing from Courses
Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.
Academic Misconduct Policy
All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.
This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at email@example.com.
Students with Disabilities - Accommodations and Accessibility
Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.
For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, firstname.lastname@example.org.
Student Conduct Code
The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically.
For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/
JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity.
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).
When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.