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Abstract
This paper examines the Kepler 2-body problem as an example of the symplectic differential geometric formulation of Hamiltonian mechanics. First, the foundations of symplectic differential geometry and the conventional analysis of the Kepler problem are presented. Then, the SO(4) and SO(3,1) symmetry of the problem and the conserved angular momentum and Runge-Lenz vectors are discussed. The symmetry is also discussed globally, and the integral curves of the Runge-Lenz vector are found.
| Dokumententyp: | Hochschulschrift (Diplomarbeit) |
|---|---|
| Keywords: | Kepler; differential geometry |
| Fakultät: | Physik > Studienabschlussarbeiten |
| Themengebiete: | 500 Naturwissenschaften und Mathematik > 500 Naturwissenschaften
500 Naturwissenschaften und Mathematik > 530 Physik |
| URN: | urn:nbn:de:bvb:19-epub-31714-5 |
| Bemerkung: | Diplomarbeit in der deutschen Version 1973: http://nbn-resolving.de/urn:nbn:de:bvb:19-epub-21922-0 |
| Sprache: | Englisch |
| Dokumenten ID: | 31714 |
| Datum der Veröffentlichung auf Open Access LMU: | 10. Jan. 2017, 14:29 |
| Letzte Änderungen: | 04. Nov. 2020, 13:08 |
| Literaturliste: | 1 Abraham, R. H. and J. E. Marsden (1967). "Foundations of Mechanics: a Mathematical Exposition of Classical Mechanics With an Introduction to the Qualitative Theory of Dynamical Systems and Applications to the Three-Body Problem." Benjamin, New York. 2 Bacry, H. (1966). "The de Sitter group L4,1 and the Bound States of Hydrogen Atom." Il Nuovo Cimento A (1965-1970) 41(2): 222-234. 3 Bander, M. and C. Itzykson (1966). "Group Theory and the Hydrogen Atom (I&II)." Reviews of Modern Physics 38(2): 330-345&346-358. 4 Dieudonné, J. (1971). "Elements d'Analyse." 5 Dirac, P. (1947). "The Principles of Quantum Mechanics." The International Series of Monographs on Physics, Oxford: Clarendon Press. 6 Györgyi, G. (1968). "Kepler’s Equation, Fock Variables, Bacry’s Generators and Dirac Brackets." Il Nuovo Cimento A Series 10 53(3): 717-736 and 62A: 449. 7 Jost, R. (1964). "Poisson Brackets (an Unpedagogical Lecture)." Reviews of Modern Physics 36(2): 572-579. 8 Kamke, E. (1956). Differentialgleichungen Reeller Funktionen, 3. Auflage; Akademische Verlagsgesellchaft, Leipzig. 9 Kostant, B. (1970). Quantization and Unitary Representations. Lectures in Modern Analysis and Applications III. C. T. Taam. Berlin, Heidelberg, Springer Berlin Heidelberg: 87-208. 10 Moser, J. (1970). "Regularization of Kepler's Problem and the Averaging Method on a Manifold." Communications on Pure and Applied Mathematics 23(4): 609-636. 11 Pauli, W. (1953). "On the Hamiltonian Structure of Non-Local Field Theories." Il Nuovo Cimento (1943-1954) 10(5): 648-667. 12 Rottmann, K. (1960). "Mathematische Formelsammlung." Bibliographisches Institut-Hochschultaschenbuecher, Mannheim: Bibliographisches Institut, 2. Auflage. 13 Ryshik, I. u. IS Gradstein (1957). Summen-, Produkt-und Integraltafeln. Berlin: VEB, Deutscher Verlag der Wissenschaften. 14 Segal, I. (1960). "Quantization of Nonlinear Systems." Journal of Mathematical Physics 1(6): 468-488. |
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