UNIK4540 – Mathematical modelling of dynamic systems
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
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Prerequisites
Formal prerequisite knowledge
None.
Recommended previous knowledge
MAT1110-Kalkulus og line?r algebra, MAT1120-Line?r algebra, MAT-INF1310-Ordinary differential equations, MAT2310-Optimal kontrollteori, INF-MAT4350 – Numerisk line?r 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
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.