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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
Teaching methods:	full-time

Guarantor:	doc. RNDr. Leoš Dvořák, CSc.
Classification:	Physics > Teaching
Is incompatible with:	NFUF202
Is interchangeable with:	NFUF202

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_KDF (14.05.2012)

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.

Aim of the course -

Last update: T_KVOF (28.03.2008)

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

Course completion requirements - Czech

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

Ústní zkouška. (Lze mít 2 opravné termíny.)

Literature - Czech

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

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

Teaching methods - Czech

Last update: T_KVOF (28.03.2008)

přednáška

Requirements to the exam - Czech

Last update: doc. RNDr. Leoš Dvořák, CSc. (05.05.2020)

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

Syllabus -

Last update: T_KDF (14.05.2012)

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.

Learning resources - Czech

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