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
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
MATHEMATICS: Vector and tensor analysis.
Rules for evaluation and completion of the course
Attendance at seminars is required and recorded by the tutor. Missed seminars have to be compensated.
Aims
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
Prerequisites and corequisites
- compulsory prerequisite
General Physics I (Mechanics and Molecular Physics)
Basic literature
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
Landau L. D., Lifshic E. M.: Mechanics. Butterworth-Heineman, 2001 (EN)
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
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
Teacher / Lecturer
Syllabus