F5510 Analytical mechanics

Faculty of Science
Autumn 2012
Extent and Intensity
2/1/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Klaus Bering Larsen, Ph.D. (lecturer)
doc. Klaus Bering Larsen, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: doc. Klaus Bering Larsen, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Wed 12:00–13:50 FLenc,03028, Wed 14:00–14:50 FLenc,03028
Prerequisites
Knowledge of elementary classical mechanics, electrodynamics and special relativity.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The Lagrangian and Hamiltonian formalism in classical mechanics and relativistic field theory; variational principles; symmetry, conservation laws and Noether's theorems; Poisson brackets; canonical transformations; Hamilton-Jacobi theory; the canonical and symmetrical tensors of energy-momentum, connections between classical and quantum mechanics, the mathematical fundament of general theory of relativity. The main aim of this lecture is: to understand the formal basis of modern theoretical physics; to acquire connections between symmetries, conservation laws and equations of motion; to obtain ability to read contemporary physical literature.
Syllabus
  • Lagrangian formalism in the classical mechanics
  • First theorem of E. Noether in the classical mechanics
  • Lagrangian formalism in the field theory
  • Connections between symmetries, conservation laws and field equations
  • Second theorem of E. Noether
  • Energy-momentum tensors
  • Hamiltonian formalism, Poisson brackets, canonical transformations
  • Hamilton-Jacobi equation
  • Connection between classical mechanics, quantum mechanics and statistical physics
  • Mathematical foundations of general theory of relativity
Literature
  • KRUPKA, Demeter. Lectures on differential invariants. Edited by Josef Janyška. Vyd. 1. Brno: Univerzita J.E. Purkyně, 1990, 193 s. ISBN 8021001658. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. The classical theory of fields. Translated by Morton Hamermesh. 4th rev. Engl. ed. Oxford: Elsevier Butterworth-Heinemann, 1975, xiii, 428. ISBN 0-7506-2768-9. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
Teaching methods
two theoretical lectures, one exercise (solving problems)/a week
Assessment methods
credit for appropriate participation in the exercizes; oral exam.
Language of instruction
English
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2012, recent)
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