Buch, Englisch, 184 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 471 g
Buch, Englisch, 184 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 471 g
Reihe: Astrophysics and Space Science Library
ISBN: 978-1-4020-1521-2
Verlag: Springer Netherlands
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Naturwissenschaften Physik Mechanik
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
- Naturwissenschaften Astronomie Astrophysik
- Naturwissenschaften Physik Angewandte Physik Astrophysik
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
Weitere Infos & Material
1 Basic Concepts and Theorems.- 2 Generalization of the Kepler Problem to Spaces of Constant Curvature.- 3 The Two-Center Problem on a Sphere.- 4 The Two-Center Problem in the Lobachevsky Space.- 5 Motion in Newtonian and Homogeneous Field in the Lobachevsky Space.
