FY546: Advanced Mechanics and Relativity Theory
Comment
Entry requirements
Academic preconditions
Course introduction
- Give the competence to handle complex problems and independently take part in interdisciplinary work and identify needs for and structure of own learning.
- Give skills to apply physical principles and mathematical tools to formulate and evaluate physical models.
- Give knowledge and understanding of the behavior of discrete particles and contiunous matter.
Applications:
The study of classical mechanics in general, and fluid dynamics in particular, is crucial for our ability to sustainably take advantage of the earth's energy resources using e.g. hydroelectric dams and wind mills. In these two cases we may regard water and air respectively as the driving fluid of the machine, and the motion of the fluid (and thus the extracted energy) is governed by the Navier-Stokes equation which is a primary focus of the second part of the course.
Expected learning outcome
- Apply the mathematical formalism of classical physics, special relativity and fluid mechanics to formulate and solve physical problems. The course theme is thus to apply Newton’s laws of motion under more general circumstances than point mechanics.
Content
- Special relativity: The Lorentz transformations, the geometry of spacetime, relativistic kinematics and dynamics.
- Central conservative force fields: Conservation of momentum and energy as a principle, Kepler’s laws and the solar system.
- Accelerated coordinate frames: Fictitious forces, the Foucault pendulum, and Newton's bucket.
- Analytical mechanics: Lagrange's and Hamilton's equations.
- Particles and rigid bodies: Energy, momentum, angular momentum; center of gravity and moment of inertia.
- Continuum mechanics: Pressure and stress, bouyancy, incompressible fluids, the Navier-Stokes equation for ideal and viscous fluids.
Literature
J.M. Knudsen and P.H. Hjorth: Elements of Newtonian Mechanics, Springer.
B. Lautrup: Physics of Continuous Matter, Second Edition: Exotic and Everyday Phenomena in the Macro-scopic World, CRC Press
Lecture notes.
See itslearning for syllabus lists and additional literature references.
Examination regulations
Exam element a)
Timing
Tests
Written exam
EKA
Assessment
Grading
Identification
Language
Duration
Examination aids
ECTS value
Indicative number of lessons
Teaching Method
The teaching method is based on three phase model.
- Intro phase: 54 hours
- Skills training phase: 36 hours, hereof tutorials: 36 hours
The teaching format is lectures and computational classes (eksaminatorietimer). In the computational classes the students solve problems and are trained in applying the theory taught in the course to explicit physical problems within the course topics. Furthermore, it is possible to hand in a number of optional assignments. Each week the lectures are followed by computational classes.
Activities in the study phase
- Solving problems prior to the tutorials.
- Self-study of the textbook.
- Prepration for the exam.