Classical mechanics

Physics, First Cycle
Educational Physics
2 year
Hours per week – 2. semester:

Enrolment status.
Final oral examination pending on succesfully completed written exam with problem solving.

Content (Syllabus outline)

Newton's mechanics: Noninertial systems and system forces. System of particles: total momentum, angular momentum and energy. Nonconservative forces.
Langrangian mechanics: Constraints and generalised coordinates. D'Alembert principle. Lagrangian and Lagrange equations. Conserved quantities. Hamilton's variational principle. Variational derivation of Lagrange equations.
Central force problem: Reduction of two-body problem. Orbits of motion. Kepler problem: orbits, Binet's relation, Kepler laws.
Motion of the rigid body: Rigid body coordinates, Euler angles. Equations of motion for a rigid body with a fixed point - free motion. Motion of the spinning top.
Small vibrations: expansion around the stationary solution. Harmonic vibrations, normal coordinates.
Hamiltonian mechanics: Legendre transformation. Hamilton's equations of motion. Example: particle in electromagnetic field. Poisson bracket. Canonical transformation.
Continuum mechanics: Longitudinal vibrations of elastic rod. Lagrange density. Variational formulation of continuum mechanics. Hamiltoniam for a continuum.


H. Goldstein, Classical Mechanics. Wiley, 1981.
L. N. Hand, J. D. Finch, Analytical Mechanics. Cambridge University Press, 1998.
P. Prelovšek, Klasična mehanika, spletna skripta FMF (2013).

Objectives and competences

The generalization of the classical mechanics of point particles, many-body systems, rigid bodies and continua.

Intended learning outcomes

Knowledge and understanding:
The description of motion of a point body, rigid body and physical continuum, as well as the many-body system. Unification of mechanics based on the Lagrange and Hamilton formalism.

Lagrange and Hamilton formulation are the basis for the description of dynamical systems, and for quantum and statistical physics of particles and fields.

General fomulation of classical mechanics within the Langrange and Hamilton formalism.

Transferable skills:
Formulation of problems in classical mechanics and methods of solution of equations of motion.

Learning and teaching methods

Lectures, exercises, homeworks and consulations.


2 tests or a written exam with problems.
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

Prof.dr. P. Prelovšek
Transport and Conservation Laws, X. Zotos, F. Naef and P. Prelovšek,
Physical Review B 55, 11029 (1997).
Spin Hydrodynamics in the S=1/2 Anisotropic Heisenberg Chain, J. Herbrych, R.
Steinigeweg, and P. Prelovšek, Physical Review B 86, 115106 (2012).
Ground State and Finite Temperature Lanczos Methods, P. Prelovšek and J.
in Strongly Correlated Systems - Numerical Methods, eds. A. Avella and
F. Mancini (Springer Series in Solid State Sciences 176, Berlin), p. 1 - 29 (2013).
Prof.dr. R. Podgornik
1. REBERNIK RIBIČ, Primož, PODGORNIK, Rudolf. Interaction of a point charge
with the surface of a uniaxial dielectric. Europhys. lett., 2013, vol. 102, no. 2,
str. 24001-p1-24001-p6, doi: 10.1209/0295-5075/102/24001. [COBISS-SI-ID
2. DEAN, David S., PARSEGIAN, Vozken Adrian, PODGORNIK, Rudolf. Fluctuation
of thermal van der Waals forces due to dipole fluctuations. Phys. rev., A, 2013,
vol. 87, iss. 3, str. 032111-1-032111-5. [COBISS-SI-ID 2545252]
3. SARABADANI, Jalal, NAJI, Ali, ASGARI, Reza, PODGORNIK, Rudolf. Erratum:
Many-body effects in the van der Waals-Casimir interaction between graphene
layers [Phys. Rev. B 84, 155407 (2011)]. Phys. rev., B, Condens. matter mater.
phys., 2013, vol. 87, iss. 23, str. 239905-1-239905-2., doi:
10.1103/PhysRevB.87.239905. [COBISS-SI-ID 2567780]
4. RAJTER, Rick F., FRENCH, Roger H., CHING, Wai-Yim, PODGORNIK, Rudolf,
PARSEGIAN, Vozken Adrian. Chirality-dependent properties of carbon
nanotubes : electronic structure, optical dispersion properties, Hamaker
coefficients and van der Waals-London dispersion interactions. RSC advances,
2013, vol. 3, iss. 3, str. 823-842., doi:
10.1039/C2RA20083J. [COBISS-SI-ID 2513508]
5. NAJI, Ali, SARABADANI, Jalal, DEAN, David S., PODGORNIK, Rudolf. Sampleto-
sample torque fluctuations in a system of coaxial randomly charged
surfaces. The European physical journal. E, Soft matter, 2012, vol. 35, no. 3, 7
str. [COBISS-SI-ID 2431076]