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. HamiltonJacobi 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 stressstrain 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 8020007725.

Horský J., Novotný J., Štefaník M. Mechanika ve fyzice. Academia, 2001.

Obetková V., Mamrillová A., Košinárová A. Teoretická mechanika. Alfa Bratislava, 1990.
