Theoretical Mechanics and Continuum Mechanics (FSI-TMM)

Academic year 2020/2021
Supervisor: doc. Ing. Radek Kalousek, Ph.D.  
Supervising institute: ÚFI all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
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.
Learning outcomes and competences:
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.
Prerequisites:
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.

Links to other subjects:
compulsory prerequisite: General Physics I (Mechanics and Molecular Physics) [TF1]
Course contents:
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).
Teaching methods and criteria:
The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.
Assesment methods and criteria linked to learning outcomes:
The exam is combined (written and oral).
Controlled participation in lessons:
Attendance at seminars is required and recorded by the tutor. Missed seminars have to be compensated.
Type of course unit:
    Lecture  13 × 3 hrs. optionally                  
    Exercise  13 × 2 hrs. compulsory                  
Course curriculum:
    Lecture 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 Solving of the problems and excercises defined in the lectures.
Literature - fundamental:
1. Landau L. D., Lifshic E. M.: Mechanics. Butterworth-Heineman, 2001
2. Landau L. D., Lifshic E. M.: Theory of elasticity. Butterworth-Heineman, 2001
3. FEYNMAN, R.P.-LEIGHTON, R.B.-SANDS, M.: Feynmanovy přednášky z fyziky, Fragment, 2001
4. Hand L. N., Finch J. D.: Analitical Mechanics. CUP, 1998.
5. Brdička M., Hladík A.: Teoretická mechanika. Academia, Praha 1987.
6. Brdička M., Samek L., Sopko B.: Mechanika kontinua. Academia, Praha 2000.
Literature - recommended:
1. Landau L. D., Lifshic E. M.: Mechanics. Butterworth-Heineman, 2001
2. Brdička M., Samek L., Sopko B.: Mechanika kontinua. Academia, Praha 2000.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
B-FIN-P full-time study --- no specialisation -- Cr,Ex 6 Compulsory 1 2 W