Course syllabus

Course-PM

MMA092 Rigid body dynamics lp2 HT21 (7.5 hp)

This course is offered by the Department of Mechanics and Maritime Sciences, Division of Dynamics

Contact details

Teachers

Petri Piiroinen, e-mail: petri.piiroinen@chalmers.se (examiner)

Björn Pålsson, e-mail: bjorn.palsson@chalmers.se (computer sessions)

Ata Jafarzadeh, e-mail: jata@chalmers.se (problem-solving and computer sessions)

Department

Mechanics and Maritime Sciences, Div Dynamics.

Visit: Hörsalsvägen 7A, Floor 3

To contact: Use email or visit us (Petri, Björn and Ata have office in same corridor). Do not use chat or inside-canvas messaging as it is not as frequently read.

Course purpose

Many mechanical systems, such as cars and robots, exhibit a much more complicated, three-dimensional motion than those treated in basic courses in mechanics. Many degrees-of-freedom, complicated constraints, three-dimensional rotations, coupled oscillations, and stability problems are among the complications that may occur. This course gives tools needed to analyse such problems. Apart from analytical methods, a software for simulating complicated dynamical systems is also introduced. The course includes several smaller tasks and a large, more real-world project, which uses both analytical methods and software.

Schedule

TimEdit (Links to an external site.)

Course literature

Boström: Rigid body dynamics (compendium)

This book will be printed, handed out and can be collected at M2 dept free of charge. It will also be posted as pdf on Canvas.

Shabana: Dynamics of Multibody Systems (e-book)

This book is available as e-book via Chalmers Library

M.M. Japp: Formulas in mechanics

The sheet of formulas will be distributed together with written exam. It will Will also be posted as pdf on this site.

Course design

The scheduled teaching activities involves lectures (L), problem-solving sessions (P) and computer class (with teachers in the computer labs answering questions), see course summary below or the calendar. A major part of the course is the work with hand-ins, which includes numerical and analytical solution of a set of dynamics problems, illustrating course topics.

Lectures (chapter in Boström compendium):

Lecture	Teacher	Topic	Boström	Self-study problems	Shabana
L1-2	Petri	Introduction, Particle dynamics	1.1-5	1.4, 1.7, 1.9	1.2-3
L3	Petri	System of particles	1.5-6	1.15	1.2-3
L4	Petri	Planar motion kinetics (Newton formulation)	4.5	4.5, 4.6	1.4
L5	Petri	Planar motion kinetics (Lagrange formulation)	5.1-2	5.4, 5.6, 5.10	1.6, 3.1-4
L6	Petri	Rotating coordinate frames, Angular velocity and acceleration	2.1-2	2.1	2
L7	Petri	Rigid body kinematic	3.1-2	3.1, 3.3, 3.4, 3.6, 3.9	2
L8	Petri	Rigid body kinematic, constraints	3.3-4		1.6, 3.1
L9	Petri	Relative motion	2.2-3	2.4, 2.7, 2.9	2.5
L10	Petri	Newton's laws for rigid bodies	4.1-3	4.9, 4.10, 4.12, 4.15
L11	Petri	Newton's laws for rigid bodies (special cases)	4.4-7	4.17, 4.18, 4.19
L12	Petri	Lagrange's equations for multibody system;	5.1-2	5.2, 5.11	3
L13	Petri	Lagrange's equations, linearizations	5.2-3		3
L14	Petri	Coupled oscillations, modal analysis	6.1-2	6.2, 6.8, 6.9,  6.10
L15	Petri	Course summary and outlook

Problem-solving sessions:

Session	Problems solved
P1	1.8, 1.12, 1.16
P2	4.2, 5.1
P3	4.3, 5.3, 5.5, 5.12
P4	3.2, 3.5, 3.7, 3.10
P5	2.8, 2.10, 2.11, 4.1
P6	4.7, 4.11, 4.13
P7	4.5, 4.16, 4.21
P8	5.7, 5.8, 5.9
P9	6.1, 6.4, 6.7, 6.11
P10	Old exam problem

 

Changes made since the last year

The lectures and examination are back to normality in that lectures, problem-solving sessions, computer labs and the examination will take place on campus. Assignment hand-ins will be uploaded and corrected on Canvas.

Learning objectives and syllabus

After completion of the course the student should be able to

- Use advanced kinematics, such as generalized coordinates, rotation matrices, relative motion, Euler angles, and various constraints (joints, rolling, etc).

- Apply Newton's and Lagrange's equations of motion to mechanical systems composed of particles and rigid bodies.

- Calculate eigenfrequencies and modal vectors for mechanical systems characterized by linearized equations of motion.

- Work with commercial software for mechanical systems in simple cases.

- Apply the learned skills to a complex mechanical problem, such as a car suspension or a robot, and show this ability by working with such a problem both analytically and with software.

Link to the syllabus on Studieportalen (please note that examination form has changed).

Study plan (Links to an external site.)

If the course is a joint course (Chalmers and Göteborgs Universitet) you should link to both syllabus (Chalmers and Göteborgs Universitet).

Examination form

The examination of the course is a combination of a written exam and five assignments/hand-ins with both analytical and simulation parts.

Assignment	Deadline	Mandatory part	Supplementary part
A1	Week 3	yes	No
A2	Week 4	yes	1 p
A3	Week 5	yes	1 p
A4	Week 6	yes	1 p
A5	Week 7 (Thursday)	no	2 p

 

The 5 assignments A1-A5 contain mandatory parts required to pass the course and supplementary parts. The supplementary parts together give a maximum of 5 bonus points to add to the final exam. A1 has only a mandatory part; A2-A4 has a mandatory part and supplementary part giving 1 point each, while A5 only has a  supplementary part that gives up to 2 points. The assignments are made available on Mondays week 2-6, and to be submitted Wednesday the following week (except A5, which is due on the Thursday). The assignments are to be done and submitted individually and will be corrected. Errors in the mandatory part will require re-submission.

The written exam consists of four problems of the type solved on the problem-solving sessions and within the project work. Each problem on the exam can give up to 5 points. Bonus points from the supplementary parts of the assignments are added to the exam score. The course grade is determined as follows:

Points (incl. bonus)	8-12	13-17	18-25
Grade	3	4	5