TEK4040 – Mathematical Modelling of Dynamic Systems

Schedule, syllabus and examination date

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Course content

The main part of the course presents the mathematics to describe the dynamic of rigid bodies. This includes how vectors and linear operators are represented by matrices. Then, the direction cosine matrices and rotation matrices are defined and interpreted, and the direction cosine matrix differential equation, rotation matrix representations and relative motion are presented.

The mathematical part is then used to understand how physical forces on rigid bodies yield their motion. This part presents angular momentum for rigid bodies, geometric description of torque-free movements for general and axes-symmetric rigid bodies, in addition to examination of the stability of rotation.

The final part of the course is an introduction to modelling of manipulators, inertial navigation systems and aircrafts.

Learning outcome

After completing the course, you will have the knowledge to

  • understand the process of modelling rigid bodies
  • understand and use Newtons laws and Angular momentum in modelling rigid bodies
  • derive mathematical models of robots, aircrafts and inertial navigation systems
  • understand how the physical forces impact the motion of rigid bodies
  • use the mathematical models in analysis, simulation, estimation and control tasks

Admission to the course

Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

Nordic citizens and applicants residing in the Nordic countries may apply to take this course as a single course student.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants.

The course builds on previous knowledge from MAT1110 – Calculus and Linear Algebra, MAT1120 – Linear Algebra, MAT-INF1310 – Ordinary differential equations (discontinued), MAT2310 – Optimal control theory (discontinued) and INF-MAT4350 – Numerical linear algebra (discontinued).

Overlapping courses


The teaching includes 3 hours of lectures each week throghout the semester.

There is one mandatory assignment which must be approved in order for you to sit the final exam.


  • The course has one mandatory assignment, which must be approved before you can sit the final exam.
  • A final oral exam counts 100% towards the final grade.

In case of a large number of students the examination may be written.

When writing your exercises make sure to familiarize yourself with the rules for use of sources and citations. Breach of these rules may lead to suspicion of attempted cheating.

It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for (one of) the following course(s):

Examination support material

You are admitted to use a UiO-approved calculator.

Language of examination

Courses taught in English will only offer the exam paper in English. You may write your examination paper in Norwegian, Swedish, Danish or English.

Grading scale

Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.

Resit an examination

Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.

Re-scheduled examinations are not offered to students who withdraw during, or did not pass, the original examination.

Special examination arrangements, use of sources, explanations and appeals

See more about examinations at UiO

Last updated from FS (Common Student System) Sep. 28, 2022 11:23:22 AM

Facts about this course

Teaching language
Norwegian (English on request)