Search programme

​Use the search function to search amongst programmes at Chalmers. The study programme and the study programme syllabus relating to your studies are generally from the academic year you began your studies.

Syllabus for

Academic year
MMA092 - Rigid body dynamics
Stelkroppsdynamik
 
Syllabus adopted 2020-02-10 by Head of Programme (or corresponding)
Owner: MPAME
7,5 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: Second-cycle
Major subject: Automation and Mechatronics Engineering, Mechanical Engineering, Engineering Physics
Department: 30 - MECHANICS AND MARITIME SCIENCES


Teaching language: English
Application code: 03116
Open for exchange students: Yes
Block schedule: B+

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0107 Examination 7,5c Grading: TH   7,5c   14 Jan 2021 am J,  09 Apr 2021 am J,  27 Aug 2021 pm J

In programs

MPAME APPLIED MECHANICS, MSC PROGR, Year 1 (compulsory elective)
MPAME APPLIED MECHANICS, MSC PROGR, Year 2 (elective)
MPAUT AUTOMOTIVE ENGINEERING, MSC PROGR, Year 2 (elective)
MPPDE PRODUCT DEVELOPMENT, MSC PROGR, Year 2 (elective)
MPSYS SYSTEMS, CONTROL AND MECHATRONICS, MSC PROGR, Year 1 (elective)
MPSYS SYSTEMS, CONTROL AND MECHATRONICS, MSC PROGR, Year 2 (elective)

Examiner:

Håkan Johansson

  Go to Course Homepage


Eligibility

General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

Mathematics, in particular linear algebra, integrals and differential equations, and mechanics, in particular dynamics of particles and planar motion of rigid bodies.

Aim

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 the tools needed to analyse such problems. Apart from analytical methods, also software for simulating complicated dynamical systems is introduced. The course includes a large, more real world project, which uses both analytical methods and software.

Learning outcomes (after completion of the course the student should be able to)

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.

Content

Particles and systems of particles: kinematics, Newton's laws, conservation laws, oscillations, stability.
Relative motion: rotation matrices, angular velocity and acceleration, motion in moving reference systems.
Rigid body kinematics: Euler angles and rotation parameterizations, constraints, rolling.
Newton's and Lagrange's equations for rigid bodies and systems: planar and three-dimensional motion, gyroscopic motion.
Coupled oscillations: linearization, eigenfrequencies, stability, modal analysis.
Introduction to simulation software.

Organisation

Lectures, problem-solving sessions and supervision. Project work runs through the whole course and includes analytical work, numerical computations, and simulations in commercial software.

Literature

To be announced.

Examination including compulsory elements

Written exam and project work. Grading: TH - Fail, 3, 4 ,5.


Published: Mon 28 Nov 2016.