Integrable systems of classical mechanics Lie algebras, Volume I: Volume I
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1990
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is designed to expose from a general and universal standpoint a variety of methods and results concerning integrable systems of classical mechanics. By such systems we mean Hamiltonian systems with a finite number of degrees of freedom possessing sufficiently many conserved quantities (integrals of motion) so that in principle integration of the corresponding equations of motion can be reduced to quadratures, i.e. to evaluating integrals of known functions. The investigation of these systems was an important line of study in the last century which, among other things, stimulated the appearance of the theory of Lie groups. Early in our century, however, the work of H. Poincare made it clear that global integrals of motion for Hamiltonian systems exist only in exceptional cases, and the interest in integrable systems declined. Until recently, only a small number ofsuch systems with two or more degrees of freedom were known. In the last fifteen years, however, remarkable progress has been made in this direction due to the invention by Gardner, Greene, Kruskal, and Miura [GGKM 19671 of a new approach to the integration of nonlinear evolution equations known as the inverse scattering method or the method of isospectral deformations. Applied to problems of mechanics this method revealed the complete integrability of numerous classical systems. It should be pointed out that all systems of this kind discovered so far are related to Lie algebras, although often this relationship is not so simple as the one expressed by the well-known theorem of E. Noether |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9783034892575 9783764323363 |
| DOI: | 10.1007/978-3-0348-9257-5 |
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| illustrated | Not Illustrated |
| indexdate | 2024-09-10T00:14:02Z |
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| isbn | 9783034892575 9783764323363 |
| language | English |
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| spelling | Perelomov, Askolʹd M. 1935- Verfasser (DE-588)11069547X aut Integrable systems of classical mechanics Lie algebras, Volume I by A. M. Perelomov Basel Birkhäuser Basel 1990 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier This book is designed to expose from a general and universal standpoint a variety of methods and results concerning integrable systems of classical mechanics. By such systems we mean Hamiltonian systems with a finite number of degrees of freedom possessing sufficiently many conserved quantities (integrals of motion) so that in principle integration of the corresponding equations of motion can be reduced to quadratures, i.e. to evaluating integrals of known functions. The investigation of these systems was an important line of study in the last century which, among other things, stimulated the appearance of the theory of Lie groups. Early in our century, however, the work of H. Poincare made it clear that global integrals of motion for Hamiltonian systems exist only in exceptional cases, and the interest in integrable systems declined. Until recently, only a small number ofsuch systems with two or more degrees of freedom were known. In the last fifteen years, however, remarkable progress has been made in this direction due to the invention by Gardner, Greene, Kruskal, and Miura [GGKM 19671 of a new approach to the integration of nonlinear evolution equations known as the inverse scattering method or the method of isospectral deformations. Applied to problems of mechanics this method revealed the complete integrability of numerous classical systems. It should be pointed out that all systems of this kind discovered so far are related to Lie algebras, although often this relationship is not so simple as the one expressed by the well-known theorem of E. Noether Physics Mathematics Mechanics Mathematics, general Mathematik https://doi.org/10.1007/978-3-0348-9257-5 Verlag Volltext |
| spellingShingle | Perelomov, Askolʹd M. 1935- Integrable systems of classical mechanics Lie algebras, Volume I Physics Mathematics Mechanics Mathematics, general Mathematik |
| title | Integrable systems of classical mechanics Lie algebras, Volume I |
| title_auth | Integrable systems of classical mechanics Lie algebras, Volume I |
| title_exact_search | Integrable systems of classical mechanics Lie algebras, Volume I |
| title_full | Integrable systems of classical mechanics Lie algebras, Volume I by A. M. Perelomov |
| title_fullStr | Integrable systems of classical mechanics Lie algebras, Volume I by A. M. Perelomov |
| title_full_unstemmed | Integrable systems of classical mechanics Lie algebras, Volume I by A. M. Perelomov |
| title_short | Integrable systems of classical mechanics Lie algebras, Volume I |
| title_sort | integrable systems of classical mechanics lie algebras volume i |
| title_sub | Volume I |
| topic | Physics Mathematics Mechanics Mathematics, general Mathematik |
| topic_facet | Physics Mathematics Mechanics Mathematics, general Mathematik |
| url | https://doi.org/10.1007/978-3-0348-9257-5 |
| work_keys_str_mv | AT perelomovaskolʹdm integrablesystemsofclassicalmechanicsliealgebrasvolumei |