Analytical Mechanics

Garant předmětu:

Petr Novotný

Lecturer:

Jiří Hrivnák, Petr Novotný

Tutor:

Jiří Hrivnák, Petr Novotný, Filip Petrásek, Stanislav Skoupý

Supervisor:

Department of Physics

Synopsis:

The course is an introduction to analytical mechanics. The students acquire knowledge of the basic concepts of the Lagrange and Hamiltonian formalism as well as diferent approaches to description of dynamics (Newton’s, Lagrange, Hamilton and Hamilton-Jacobi equations). The efficiency of these methods 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.

Requirements:

02MECHZ

Syllabus of lectures:

1. Mathematical formalism

2. Newtonian mechanics

3. The Lagrange function, constraints, generalized coordinates 4. Lagrange equations

5. Symmetries of the Lagrange function and conservation laws 6. Static equilibrium, the principle of virtual displacements

7. Differential principles

8. Integral principles

9. Hamilton's formalism

10. Poisson bracket and conservation laws

11. Canonical transformations

12. Hamilton-Jacobi equation

Syllabus of tutorials:

Solving problems to illustrate the theory from the lecture.

Study Objective:

Knowledge:

Learn the basics of analytical mechanics, Lagrange and Hamilton formalism.

Skills:

Solving problems in mechanics with Lagrange and Hamilton formalism

Study materials:

Key references:

[1] L.D. Landau, E.M. Lifšic, Course of Theoretical Physics, Elsevier, 2013

[2] F. Strocchi, A Primer of Analytical Mechanics, Springer International, New York 2018

Recommended references:

[3] G. Joos, I. Freeman: Theoretical Physics, Courier Corp. 2013.

Note:

Time-table for winter semester 2022/2023:

Time-table is not available yet

Time-table for summer semester 2022/2023:

Time-table is not available yet

The course is a part of the following study plans: