UČNI NAČRT PREDMETA/COURSE SYLLABUS Predmet: Klasična mehanika

Course title: Classical mechanics

Študijski programi in stopnja Študijska smer Letnik Semestri

Fizika, prva stopnja, univerzitetni Fizika (smer) 2. letnik Letni

Univerzitetna koda predmeta/University course code: 1155

Predavanja Seminar Vaje Klinične vaje Druge oblike študija

Samostojno delo

ECTS

30 0 30 0 0 90 5

Nosilec predmeta/Lecturer: Peter Prelovšek, Rudi Podgornik

Vrsta predmeta/Course type: obvezni/compulsory

Jeziki/Languages: Predavanja/Lectures: Slovenščina

Vaje/Tutorial: Slovenščina

Pogoji za vključitev v delo oz. za opravljanje študijskih obveznosti:

Prerequisites:

Vpis v letnik. Opravljeni kolokviji oz. pisni izpit iz vaj kot pogoj za pristop k ustnemu izpitu.

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

Vsebina: Content (Syllabus outline):

Newtonove mehanika: Neinercialni sistemi in sistemske sile. Sistem delcev: gibalna količina, vrtilna količina in celotna energija. Nekonzervativne sile. Lagrangeova mehanika: Vezi in generalizirane koordinate. D'Alembertov princip. Lagrangeova funkcija in gibalne enačbe. Ohranjene količine - integrali gibanja: ciklične koordinate, energija. Hamiltonov variacijski princip. Variacijska izpeljava Langrangeovih enačb. Gibanje delca pri centralni sili: Problem dveh teles in redukcija. Krivulje gibanja - orbite. Keplerjev problem: orbite, Binetova zveza. Obhodni čas. Gibanje togega telesa: Lega togega telesa, Eulerjevi koti. Togo telo s fiksno točko: enačbe gibanja, prosto gibanje. Vpeta simetrična vrtavka. Majhna nihanja: razvoj okrog stacionarne točke. Lastna nihanja, normalne koordinate. Hamiltonova mehanika: Legendreova transformacija. Hamiltonove gibalne enačbe. Primeri: nabit delec v elektromagnetnem polju. Poissonov oklepaj. Kanonične transformacije. Dinamika zveznih sredstev: Longitudinalna nihanja elastične palice - kontinuumski popis. Langrangeova gostota. Variacijska formulacija mehanike kontinuuma. Hamiltonova funkcija za zvezno sredstvo.

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.

Temeljna literatura in viri/Readings:

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).

Cilji in kompetence: Objectives and competences:

Poglobitev in nadgraditev znanja klasične mehanike točkastega delca, sistemov delcev, togega delca in kontinua.

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

Predvideni študijski rezultati: Intended learning outcomes:

Znanje in razumevanje: Opis gibanja točkastega, togega in zveznega telesa, ter sistema teles. Poenotenje mehanike na osnovi Lagrangeovega in Hamiltonovega formalizma. Uporaba: Lagrangeov in Hamiltonov formalizem služijo kot osnova obravnave dinamičnih sistemov, ter kvantne in statistične fizike delcev in polj. Refleksija: Posplošenje klasične mehanike na osnovi Lagrangeove in Hamiltonove formulacije. Prenosljive spretnosti - niso vezane le na en predmet: Formulacija problemov klasične mehanike in metode reševanje gibalnih enačb.

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

Metode poučevanja in učenja: Learning and teaching methods:

Predavanja, vaje, domače naloge in konzultacije. Lectures, exercises, homeworks and consulations.

Načini ocenjevanja: Delež/Weight Assessment:

2 kolokvija ali pisni izpit iz nalog 2 tests or a written exam with problems.

Ustni izpit Oral exam

(ocene: 5 (negativno), 6-10 (pozitivno), ob upoštevanju Statuta UL)

grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Reference nosilca/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. Bonča, 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 2718971] 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. http://pra.aps.org/abstract/PRA/v87/i3/e032111. [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. http://prb.aps.org/abstract/PRB/v87/i23/e239905, 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. http://pubs.rsc.org/en/Content/ArticleLanding/2013/RA/C2RA20083J, 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. http://dx.doi.org/10.1140/epje/i2012-12024-y. [COBISS.SI-ID 2431076]

UČNI NAČRT PREDMETA/COURSE SYLLABUS Predmet: Klasična mehanika

Course title: Classical mechanics

Študijski programi in stopnja Študijska smer Letnik Semestri

Fizika, prva stopnja, univerzitetni Izobraževalna smer (smer) 2. letnik Letni

Univerzitetna koda predmeta/University course code: 1155

Predavanja Seminar Vaje Klinične vaje Druge oblike študija

Samostojno delo

ECTS

30 0 30 0 0 90 5

Nosilec predmeta/Lecturer: Peter Prelovšek, Rudi Podgornik

Vrsta predmeta/Course type: obvezni/compulsory

Jeziki/Languages: Predavanja/Lectures: Slovenščina

Vaje/Tutorial: Slovenščina

Pogoji za vključitev v delo oz. za opravljanje študijskih obveznosti:

Prerequisites:

Vpis v letnik. Opravljeni kolokviji oz. pisni izpit iz vaj kot pogoj za pristop k ustnemu izpitu.

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

Vsebina: Content (Syllabus outline):

Newtonove mehanika: Neinercialni sistemi in sistemske sile. Sistem delcev: gibalna količina, vrtilna količina in celotna energija. Nekonzervativne sile. Lagrangeova mehanika: Vezi in generalizirane koordinate. D'Alembertov princip. Lagrangeova funkcija in gibalne enačbe. Ohranjene količine - integrali gibanja: ciklične koordinate, energija. Hamiltonov variacijski princip. Variacijska izpeljava Langrangeovih enačb. Gibanje delca pri centralni sili: Problem dveh teles in redukcija. Krivulje gibanja - orbite. Keplerjev problem: orbite, Binetova zveza. Obhodni čas. Gibanje togega telesa: Lega togega telesa, Eulerjevi koti. Togo telo s fiksno točko: enačbe gibanja, prosto gibanje. Vpeta simetrična vrtavka. Majhna nihanja: razvoj okrog stacionarne točke. Lastna nihanja, normalne koordinate. Hamiltonova mehanika: Legendreova transformacija. Hamiltonove gibalne enačbe. Primeri: nabit delec v elektromagnetnem polju. Poissonov oklepaj. Kanonične transformacije. Dinamika zveznih sredstev: Longitudinalna nihanja elastične palice - kontinuumski popis. Langrangeova gostota. Variacijska formulacija mehanike kontinuuma. Hamiltonova funkcija za zvezno sredstvo.

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.

Temeljna literatura in viri/Readings:

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).

Cilji in kompetence: Objectives and competences:

Poglobitev in nadgraditev znanja klasične mehanike točkastega delca, sistemov delcev, togega delca in kontinua.

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

Predvideni študijski rezultati: Intended learning outcomes:

Znanje in razumevanje: Opis gibanja točkastega, togega in zveznega telesa, ter sistema teles. Poenotenje mehanike na osnovi Lagrangeovega in Hamiltonovega formalizma. Uporaba: Lagrangeov in Hamiltonov formalizem služijo kot osnova obravnave dinamičnih sistemov, ter kvantne in statistične fizike delcev in polj. Refleksija: Posplošenje klasične mehanike na osnovi Lagrangeove in Hamiltonove formulacije. Prenosljive spretnosti - niso vezane le na en predmet: Formulacija problemov klasične mehanike in metode reševanje gibalnih enačb.

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

Metode poučevanja in učenja: Learning and teaching methods:

Predavanja, vaje, domače naloge in konzultacije. Lectures, exercises, homeworks and consulations.

Načini ocenjevanja: Delež/Weight Assessment:

2 kolokvija ali pisni izpit iz nalog 2 tests or a written exam with problems.

Ustni izpit Oral exam

(ocene: 5 (negativno), 6-10 (pozitivno), ob upoštevanju Statuta UL)

grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Reference nosilca/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. Bonča, 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 2718971] 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. http://pra.aps.org/abstract/PRA/v87/i3/e032111. [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. http://prb.aps.org/abstract/PRB/v87/i23/e239905, 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. http://pubs.rsc.org/en/Content/ArticleLanding/2013/RA/C2RA20083J, 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. http://dx.doi.org/10.1140/epje/i2012-12024-y. [COBISS.SI-ID 2431076]