Integrable Problems of Celestial Mechanics in Spaces of Constant Curvature (Hardcover)

T.G. Vozmischeva

ISBN 10: 1402015216 / ISBN 13: 9781402015212

Editore: Kluwer Academic Publishers, New York, NY, 2003

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Hardcover. This book combines the study of celestial mechanics, with modern geometrical methods in physics. According to recently developed views and research, one of the basic qualitative characteristics of an integrable Hamiltonian system is a structure of the Liouville foliation. A number of interesting results have been obtained. In particular, some of the constructed topological invariants did not appear in integrable cases investigated by many researchers earlier on. The topology of the isoenergy surfaces is also strongly different from what authors presented before. Some new topological effects in the problems of dynamics on spaces of constant curvature have been discovered. This book is intended for specialists and post-graduate students in celestial mechanics, differential geometry and applications, and Hamiltonian mechanics. Introd uction The problem of integrability or nonintegrability of dynamical systems is one of the central problems of mathematics and mechanics. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Codice articolo 9781402015212

Dati bibliografici

• Titolo: Integrable Problems of Celestial Mechanics in Spaces of Constant Curvature (Hardcover)
• Editore: Kluwer Academic Publishers, New York, NY
• Data di pubblicazione: 2003
• Lingua: Inglese
• ISBN 10: 1402015216
• ISBN 13: 9781402015212
• Rilegatura: Hardcover
• Condizione: new

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Riassunto

Introd uction The problem of integrability or nonintegrability of dynamical systems is one of the central problems of mathematics and mechanics. Integrable cases are of considerable interest, since, by examining them, one can study general laws of behavior for the solutions of these systems. The classical approach to studying dynamical systems assumes a search for explicit formulas for the solutions of motion equations and then their analysis. This approach stimulated the development of new areas in mathematics, such as the al­ gebraic integration and the theory of elliptic and theta functions. In spite of this, the qualitative methods of studying dynamical systems are much actual. It was Poincare who founded the qualitative theory of differential equa­ tions. Poincare, working out qualitative methods, studied the problems of celestial mechanics and cosmology in which it is especially important to understand the behavior of trajectories of motion, i.e., the solutions of differential equations at infinite time. Namely, beginning from Poincare systems of equations (in connection with the study of the problems of ce­ lestial mechanics), the right-hand parts of which don't depend explicitly on the independent variable of time, i.e., dynamical systems, are studied.