Theoretical Physics 1

Lecturer:

Igor Jex (guarantor)

Tutor:

Jiří Hrivnák, Jaroslav Novotný, Petr Novotný, Jan Vysoký

Supervisor:

Department of Physics

Synopsis:

The course is an introduction to analytical mechanics. The students acquire knowledge of the basic concepts of the Lagrange formalism. The efficiency of this method is illustrated on elementary examples like the two-body problem, the motion of a system of constrained mass points, and of a rigid body. Advanced parts of the course cover differential and integral principles of mechanics. The subject is the first part of the course of classical theoretical physics (02TEF1, 02TEF2).

Requirements:

02MECH, 02ELMA

Syllabus of lectures:

1. Mathematical formalism

2. Newtonian mechanics

3. The Lagrange function, constraints, generalised coordinates

4. Lagrange equations

5. Symmetries of the Lagrange function and conservation laws

6. Virial theorem

7. The two-body problem

8. Oscillations of systems of mass points

9. Dynamics of rigid bodies, Euler's equations

10. Static equilibrium, the principle of virtual displacements

11. Differential principles (d´Alembert, Jourdain, Gauss, Hertz)

12 .Integral principles of Hamilton, Maupertuis and Jacobi

Syllabus of tutorials:

Solving exercises on the following topics:

1.Mathematical formalism

2.Newtonian mechanics

3.Lagrange function, constraints, generalised coordinates

4. Lagrange equations

5.Symmetries of the Lagrange function and conservation laws

6.Virial theorem

7. The two-body problem

8. Oscillations of coupled systems

9 .Dynamics of rigid bodies, Euler's equations

10. Static equilibrium, the principle of virtual displacements

11. Differential principles (d´Alembert, Jourdain, Gauss, Hertz)

12. Integral principles of Hamilton, Maupertuis and Jacobi

Study Objective:

Knowledge:

Learn the basics of analytical mechanics. The subject belongs to the course of classical theoretical physics at FNSPE.

Skills:

Application of methods of theoretical physics to solve concrete examples

Study materials:

Key references:

[1] I. Štoll, J. Tolar, I. Jex, Classical Theoretical Physics, Karolinum, Prague 2017 (in Czech)

Recommended references:

[1] V. Trkal, Mechanics of Mass Points and Solid Bodies, ČSAV, Praha 1956 (in Czech)

[2] L.D. Landau, E.M. Lifšic, Teoretičeskaja fizika I, FIZMATGIZ, Moskva 2002 (in Russian)

Note:

Time-table for winter semester 2019/2020:

Time-table is not available yet

Time-table for summer semester 2019/2020:

Time-table is not available yet

The course is a part of the following study plans:

• BS Matematické inženýrství - Matematické modelování (compulsory course of the specialization, elective course)
• BS Matematické inženýrství - Matematická fyzika (compulsory course of the specialization, elective course)
• BS Matematické inženýrství - Aplikované matematicko-stochastické metody (compulsory course of the specialization, elective course)
• BS Matematická informatika (elective course)
• BS Informatická fyzika (compulsory course of the specialization, elective course)
• BS Aplikace softwarového inženýrství (elective course)
• BS Aplikovaná informatika (elective course)
• BS jaderné inženýrství B (compulsory course of the specialization, elective course)
• BS Jaderné inženýrství C (elective course)
• BS Dozimetrie a aplikace ionizujícího záření (compulsory course of the specialization, elective course)
• BS Experimentální jaderná a částicová fyzika (compulsory course of the specialization, elective course)
• BS Radiologická technika (elective course)
• BS Inženýrství pevných látek (compulsory course of the specialization, elective course)
• BS Diagnostika materiálů (compulsory course of the specialization, elective course)
• BS Fyzika a technika termojaderné fúze (compulsory course of the specialization, elective course)
• BS Fyzikální elektronika (compulsory course of the specialization, elective course)
• Bc Laser Technology and Instrumentation (elective course)
• BS Fyzikální technika (elective course)
• BS Jaderná chemie (elective course)