# SG2126 Non-linear Oscillations and Dynamical Systems in Mechanics 7.5 credits

#### Non-linear Oscillations and Dynamical Systems in Mechanics

The student is made familiar with phenomena appearing in nonlinear dynamics and is required to perform certain analysis of nonlinear models with analytical and numerical methods.

### Offering and execution

Course offering missing for current semester as well as for previous and coming semesters

## Course information

### Content and learning outcomes

#### Course contents *

Flows and mappings, state space formulations, geometrical methods, limit sets, bifurcations, Poincaré mappings, chaos.

#### 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.

#### Course Disposition

No information inserted

### Literature and preparations

#### Specific prerequisites *

Linear algebra, multivariable calculus, ordinary differential equations, basic mechanics, numerical methods.

#### Recommended prerequisites

No information inserted

#### Equipment

No information inserted

#### Literature

Strogatz, S. H. 1994. Nonlinear Dynamics and Chaos. Addison-Wesley.

Distributed material.

### Examination and completion

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

### Further information

#### Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web SG2126

SCI/Mechanics

#### Main field of study *

Mechanical Engineering

Second cycle