Description:

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

Contents:

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

Seminar contents:

Solving problems to illustrate the theory from the lecture.

Recommended literature:

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

Keywords:

Analytical mechanics, the Lagrangian formalism, variational principles of mechanics, the Hamiltonian formalism, Hamilton's equations, Poison bracket, conservation laws, Noether?s theorem, canonical transformations, the Hamilton-Jacobi equation, d ?Alembert principle, Hamilton's principle, Jacobi principle, Liouville's theorem, Virial theorem

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar