Items related to Integrable Systems of Classical Mechanics and Lie Algebras...
This book is designed to expose from a general and universal standpoint a variety ofmethods and results concerning integrable systems ofclassical me chanics. By such systems we mean Hamiltonian systems with a finite number of degrees of freedom possessing sufficiently many conserved quantities (in tegrals ofmotion) so that in principle integration ofthe correspondingequa tions of motion can be reduced to quadratures, i.e. to evaluating integrals of known functions. The investigation of these systems was an important line ofstudy in the last century which, among other things, stimulated the appearance of the theory ofLie groups. Early in our century, however, the work ofH. 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 de grees 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 ofa new approach to the integra tion ofnonlinear evolution equations known as the inverse scattering method or the method of isospectral deformations. Applied to problems of mechanics this method revealed the complete in tegrability 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 sosimpleas the oneexpressed by the well-known theorem of E. Noether.
"synopsis" may belong to another edition of this title.
Language Notes:
Text: English (translation)
Original Language: Russian
Original Language: Russian
"About this title" may belong to another edition of this title.
- PublisherBirkhäuser
- Publication date2011
- ISBN 10 3034892586
- ISBN 13 9783034892582
- BindingPaperback
- Number of pages320
(No Available Copies)
Search Books: Create a WantIf you know the book but cannot find it on AbeBooks, we can automatically search for it on your behalf as new inventory is added. If it is added to AbeBooks by one of our member booksellers, we will notify you!
Create a Want