Course detail

# Theoretical Mechanics and Continuum Mechanics

FSI-TMMAcad. year: 2017/2018

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).

Supervisor

Department

Learning outcomes of the course unit

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.

**compulsory prerequisite**

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Landau L. D., Lifshic E. M.: Mechanics. Butterworth-Heineman, 2001 (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)

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)

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

Brdička M., Samek L., Sopko B.: Mechanika kontinua. Academia, Praha 2000. (CS)

Planned learning activities and teaching methods

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).

Language of instruction

Czech

Work placements

Not applicable.

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.

Specification of controlled education, way of implementation and compensation for absences

Attendance at seminars is required and recorded by the tutor. Missed seminars have to be compensated.

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

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)

seminars

26 hours, compulsory

Teacher / Lecturer

Syllabus

http://physics.fme.vutbr.cz/ufi.php?Action=0&Id=1051