Course: Theoretical mechanics

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Course title Theoretical mechanics
Course code KFY/TEM
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Winter and summer
Number of ECTS credits 5
Language of instruction Czech
Status of course unspecified
Form of instruction Face-to-face
Work placements Course does not contain work placement
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • Erhart Jiří, prof. Mgr. Ph.D.
Course content
Mechanics of point particle and rigid body dynamics, system of point particles. Constraints, their classification and physical meaning. Generalized coordinates. Euler' angles. Variation and variational calculus. Virtual work principle. Lagrange's equations. Hamilton's principle. Kinetic and potential energy. Lagrange's and Hamilton's function and their physical meaning. Canonical and Legendre's transformation. Poisson's brackets. Examples on application of Lagrange's and Hamilton's equation for the solution of mass point dynamics. Hamilton-Jacobi theory. Action integral. Introduction to the continuum mechanics. Tensors and their invariants. Stress/strain tensor and their physical meaning. Hook's law. Elastic constant tensor symmetry for different crystallographic classes. Equation of equilibrium and motion for continuum.

Learning activities and teaching methods
Monological explanation (lecture, presentation,briefing)
  • Class attendance - 56 hours per semester
Learning outcomes
The subject is focused to the fundamental teoretical methods applied to the mechanical systems, which are very general and could be used in many other fields, e.g. in the field theory. Variational methods, principle of the virtual work and transformations of the general coordinates are treated. In continuum mechanics, the fundamentals of the stress-strain description and symmetry of the crystallographic lattice are applied to the symmetry of tensor coordinates of elastic moduli tensor.
Fundamental knowledge of theoretical mechanics for selected topics.
Prerequisites
Fundamental course of Physics (Mechanics)

Assessment methods and criteria
Oral exam, Written exam

Activity at practical training is requirement for obtaining the credit. Successful answers to the examination questions are necessary for passing the exam.
Recommended literature
  • Brdička M., Hladík A. Teoretická mechanika. Academia Praha, 1987.
  • Brdička M. Mechanika kontinua. NČSAV Praha, 1959.
  • Brdička M.,Samek L., Sopko B. Mechanika kontinua. Academia, 2000. ISBN 80-200-0772-5.
  • Horský J., Novotný J., Štefaník M. Mechanika ve fyzice. Academia, 2001.
  • Obetková V., Mamrillová A., Košinárová A. Teoretická mechanika. Alfa Bratislava, 1990.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester