Flows and mappings, state space formulations, geometrical methods, limit sets, bifurcations, Poincaré mappings, chaos.
SG2126 Non-linear Oscillations and Dynamical Systems in Mechanics 7.5 credits
This course has been discontinued.
Last planned examination: Autumn 2022
Decision to discontinue this course:
No information insertedCourse offerings are missing for current or upcoming semesters.
Headings with content from the Course syllabus SG2126 (Autumn 2022–) are denoted with an asterisk ( )
Content and learning outcomes
Course contents
Intended learning outcomes
After the course the student should be able to:
- Explain how ordinary differential equations (ODE) and iterated maps give rise to dynamical system.
- Be able to define the state space, its limit sets and attractors.
- Explain how the state space dimension limits the possible dynamics.
- Sketch the limit set and starting from this characterize the main features in the flow of a dynamical system given by ODEs in the plane.
- Recognize and describe the result of a simulation using the concept of Poincare mapping.
- Know about and be able to calculate the fractal dimension in a few simple cases.
- Know about the concept of chaos in dynamical systems and state some properties of a chaotic dynamical system.
Literature and preparations
Specific prerequisites
English B / English 6
Linear algebra, multivariable calculus, ordinary differential equations, basic mechanics, numerical methods.
Recommended prerequisites
No information inserted
Equipment
No information inserted
Literature
No information inserted
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
A, B, C, D, E, FX, F
Examination
- INL1 - Hand in Assignments, 4.5 credits, grading scale: P, F
- TENA - Examination, 3.0 credits, grading scale: A, B, C, D, E, FX, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Opportunity to complete the requirements via supplementary examination
No information inserted
Opportunity to raise an approved grade via renewed examination
No information inserted
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information
Course room in Canvas
Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.
Offered by
Main field of study
Mechanical Engineering
Education cycle
Second cycle
Add-on studies
No information inserted
Contact
Arne Nordmark