UNIK4540 – Mathematical modelling of dynamic systems

Course description

• Course content
• Learning outcome
• Admission
• Prerequisites

• Teaching
• Examination

Course content

Vector and affine spaces. Matrix representation of vectors and linear operators. Coordinate systems (c.s.), change of c.s., direction cosine (d.c.m.) and rotation matrices (r.m.). Interpretations and the d.c.m. differential equation, r.m. representations (euler angles, angle-axis, quaterinons), relative motion. Rigid body kinematics and kinetics. Angular momentum for rigid bodies. Geometric description of torque-free movements for general and axes-symmetric rigid bodies. Modelling of manipulators: kinematics and inverse kinematics, velocity and static forces, the iterative Newton-Euler method, simulation and force calculation in n-link robots. Aircraft modelling. Modelling of inertial navigation systems: inertial sensors, navigation and error equations. Using the Kalman filter for calibration, alignment and navigation problems.

Learning outcome

The student will gain a thorough knowledge in modelling of robots, aircraft and inertial navigation systems for analysis, simulation, estimation and control tasks.

Admission

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.

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

Prerequisites

Formal prerequisite knowledge

None.

Recommended previous knowledge

MAT1110-Kalkulus og lineær algebra, MAT1120-Lineær algebra, MAT-INF1310-Ordinary differential equations, MAT2310-Optimal kontrollteori, INF-MAT4350 – Numerisk lineær algebra.

Teaching

The course will be given as crash course over two weeks or as a guided self-tuition course. The student will get a DVD containing videos of the lectures and copies of all written material including what was written on the whiteboard. The students must hand in and pass on mandatory term projects before they are admitted to take the exam.

Examination

Oral or written examination. Graded marks.

Explanations and appeals

• Explanation of grades and appeals

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.