Theoretical Physics 1

Course guarantor:

Lecturer:

Tutor:

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 (Newtons, 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. The subject is the first part of the course of classical theoretical physics (02TEF1, 02TEF2).

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. The subject belongs to the course of classical theoretical physics at FNSPE.

Skills:

Solving problems in mechanics with Lagrange and Hamilton formalism

Study materials:

Key references:

[1] H. Goldstein, C. P. Poole, J. Safko: Classical Mechanics, Pearson Education; 3rd edition, 2011

[2] L.N. Hand, J.D. Finch: Analytical mechanics, Cambridge University Press, 1998

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

Recommended references:

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

[4] A.S. Kompanayets, Theoretical Physics, Dover Publications, 2012

[5] J. R. Taylor: Classical Mechanics, University Science Books, 2005

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: