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Theoretical Mechanics - NUFY028
Title: Teoretická mechanika
Guaranteed by: Department of Physics Education (32-KDF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech
Teaching methods: full-time
Guarantor: doc. RNDr. Leoš Dvořák, CSc.
Classification: Physics > Teaching
Is incompatible with: NFUF202
Is interchangeable with: NFUF202
Annotation -
Introduction to concepts and methods of analytical mechanics and their use for solving of selected problems: The principle of virtual work, Lagrange and Hamilton equations, variational principles, kinematics and dynamics of rigid bodies, basic ideas how to describe continuous systems. For students of the 2nd year of combinations Math and Physics and Physics/Informatics.
Last update: T_KDF (14.05.2012)
Aim of the course -

Introduction to concepts and methods of analytical mechanics and their use for solving of selected problems: The principle of virtual work, Lagrange and Hamilton equations, variational principles, kinematics and dynamics of rigid bodies, basic ideas how to describe continuous systems.

For students of the 2nd year of combinations Math and Physics and Physics/Informatics for High Schools.

Last update: T_KVOF (28.03.2008)
Course completion requirements - Czech

Ústní zkouška. (Lze mít 2 opravné termíny.)

Last update: Dvořák Leoš, doc. RNDr., CSc. (10.06.2019)
Literature - Czech

Brdička M., Hladík A.: Teoretická mechanika, Academia, Praha, 1987

Brdička M.: Mechanika kontinua, Academia, Praha, 2000

Leech J. W.: Klasická mechanika, SNTL, Praha, 1970

Dvořák L.: Teoretická mechanika. Prozatímní učební text k přednášce NUFY028 pro posluchače oboru Fyzika zaměřená na vzdělávání. Dostupné online: http://kdf.mff.cuni.cz/vyuka/Teoreticka_mechanika/

Doplňková literatura:

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

Last update: Dvořák Leoš, doc. RNDr., CSc. (01.10.2017)
Teaching methods - Czech

přednáška

Last update: T_KVOF (28.03.2008)
Requirements to the exam - Czech

Při ústní zkoušce se ověřují znalosti dle sylabu přednášky. (Typicky pomocí dvou otázek.)

Last update: Dvořák Leoš, doc. RNDr., CSc. (05.05.2020)
Syllabus -
The principle of virtual work.
Configuration space, constrains, virtual displacement, applications, d'Alembert's principle. ~ Lagrange's equations. Generalized coordinates, generalized forces, Lagrangian, Lagrange's equations of the 2nd kind. Applications.

Lagrange's equations of the 1st kind.
Small oscilations of systems of point masses.
Linearization of equations. Lagrangian for small oscillations. Normal oscillations.

Motion in a central field.
2-body problem, separation of Lagrange's equations. Cyclic coordinates. Binet's formula. Scattering: Rutherford formula, scattering at rigid sphere, differential cross-section.

Hamilton's equations.
Generalized momentum, phase space. Hamiltonian (and energy). Hamilton's canonical equations.

Elements of deterministic chaos.
Determinism of classical mechanics. Stability of solution of differential equations. Attractors. Examples: a planet near a binary star, double pendulum, Lorentz attractor. Population dynamics model, doubling of periods; universality in chaos.

Variational principles.
Hamilton's principle, action. Euler-Lagrange's equations. Brachistochrone. Variational principles in other parts of physics.

Kinematics and dynamics of rigid body.
Tensor of inertia, motion of free symmetrical gyroscope.

Waves.
Equation of motion of a string and its solution.

Elements of mechanics of continuum.
Stress tensor, strain tensor, generalized Hook's law. Equation of hydrostatic equilibrium; application to spherically symmetric star. Continuity equation. Euler's hydrodynamic equations.

Last update: T_KDF (14.05.2012)
Learning resources - Czech

Dvořák L.: Teoretická mechanika. Prozatímní učební text k přednášce NUFY028 pro posluchače oboru Fyzika zaměřená na vzdělávání. Dostupné online: http://kdf.mff.cuni.cz/vyuka/Teoreticka_mechanika/

Last update: Dvořák Leoš, doc. RNDr., CSc. (01.10.2017)
 
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