Course detail

Theoretical Mechanics and Continuum Mechanics

FSI-TMMAcad. year: 2024/2025

The course represents the first part of the basic course of theoretical physics.
It is concerned with the following topics:
ANALYTICAL MECHANICS. Hamilton’s variational principle. The Lagrange equations. Conservations laws. Hamilton’s equations. Canonical transformations. Poisson brackets. Liouville’s theorem. The Hamilton-Jacobi equation. Integration of the equations of motion (Motion in one dimension. Motion in a central field. Scattering.) Small oscillations. MECHANICS OF CONTINUOUS MEDIA. The strain and stress tensor. The continuum equation. Elastic media, Hook’s law. Equilibrium of isotropic bodies. Elastic waves. Ideal fluids (the Euler equation, Bernoulli’s theorem). Viscous fluids (the Navier-Stokes equation).

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

doc. Ing. Radek Kalousek, Ph.D.

Department

Institute of Physical Engineering (ÚFI)

Entry knowledge

Knowledge of particle and continuum mechanics on the level defined by the textbook HALLIDAY, D. - RESNICK, R. - WALKER, J. Fundamentals of Physics. J. Wiley and Sons.
MATHEMATICS: Vector and tensor analysis.

Rules for evaluation and completion of the course

The exam is combined (written and oral).
Attendance at seminars is required and recorded by the tutor. Missed seminars have to be compensated.

Aims

The course objective is to provide students with basic ideas and methods of classical mechanics and enable them to be capable of applying these basics to physical systems in order to explain and predict the behaviour of such systems.
The knowledge of principles of classical mechanics (mechanics of particles and systems, and mechanics of continuous media) and ability of applying them to physical systems in order to explain and predict the behaviour of such systems.

Study aids

Not applicable.

Prerequisites and corequisites

Basic literature

Brdička M., Hladík A.: Teoretická mechanika. Academia, Praha 1987. (CS)
Brdička M., Samek L., Sopko B.: Mechanika kontinua. Academia, Praha 2000. (CS)
FEYNMAN, R.P.-LEIGHTON, R.B.-SANDS, M.: Feynmanovy přednášky z fyziky, Fragment, 2001 (CS)
Hand L. N., Finch J. D.: Analitical Mechanics. CUP, 1998. (EN)
Landau L. D., Lifshic E. M.: Mechanics. Butterworth-Heineman, 2001 (EN)
Landau L. D., Lifshic E. M.: Theory of elasticity. Butterworth-Heineman, 2001 (EN)

Recommended reading

Brdička M., Samek L., Sopko B.: Mechanika kontinua. Academia, Praha 2000. (CS)
Landau L. D., Lifshic E. M.: Mechanics. Butterworth-Heineman, 2001 (EN)

Classification of course in study plans

  • Programme B-FIN-P Bachelor's 2 year of study, winter semester, compulsory

  • Programme C-AKR-P Lifelong learning

    specialization CZS , 1 year of study, winter semester, elective

Type of course unit

 

Lecture

39 hod., optionally

Teacher / Lecturer

prof. Mgr. Tomáš Tyc, Ph.D.

Syllabus

I. MECHANICS OF PARTICLES AND SYSTEMS
A) Principles
1. Hamilton’s variational principle
2. The Lagrange equations
3. Conservations laws
4. The canonical equations (Hamilton’s equations, canonical transformations, Poisson brackets, Liouville’s theorem, the Hamilton-Jacobi equation)
B) Applications
5. Integration of the equations of motion (Motion in one dimension. Motion in a central field. Scattering.)
6. Elements of rigid body mechanics
7. Small oscillations (Eigenfrequencies, normal coordinates.)
II. MECHANICS OF CONTINUOUS MEDIA
1. The strain tensor
2. The stress tensor
3. Hook’s law
4. The thermodynamics of deformations
5. The equation of equilibrium for isotropic bodies
6. The equation of motion for an isotropic elastic medium. Elastic waves
B) Fluid mechanics
7. Kinematics of fluids
8. The continuum equation
9. The equation of motion: ideal fluids (the Euler equation, Bernoulli’s theorem), viscous fluids (the Navier-Stokes equation)

Exercise

26 hod., compulsory

Teacher / Lecturer

Ing. Pavel Procházka, Ph.D.

Syllabus

Solving of the problems and excercises defined in the lectures.