Course detail
Theoretical Mechanics and Continuum Mechanics
FSI-TMM Acad. year: 2024/2025 Winter semester
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
Supervisor
Department
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.
The study programmes with the given course
Programme B-FIN-P: Physical Engineering and Nanotechnology, Bachelor's, compulsory
Programme C-AKR-P: , Lifelong learning
specialization CZS: , elective
Type of course unit
Lecture
39 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)
Exercise
26 hours, compulsory
Teacher / Lecturer
Syllabus
Solving of the problems and excercises defined in the lectures.