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Author: G.E.O. Giacaglia Publisher: Springer Science & Business Media ISBN: 9401033234 Category : Science Languages : en Pages : 540
Book Description
The subjects of resonance and stability are closely related to the problem of evolution of the solar system. It is a physically involving problem and the methods available to mathematics today seem unsatisfactory to produce pure non linear ways of attack. The linearization process in both subjects is clearly of doubtful significance, so that, even if very restrictive, numerical solutions are still the best and more valuable sources of informations. It is quite possible that we know now very little more of the entire problem that was known to Poincare, with the advantage that we can now compute much faster and with much more precision. We feel that the papers collected in this Symposium have contributed a step forward to the comprehension of Resonance, Periodic Orbits and Stability. In a field like this, it would be a surprise if one had gone a long way toward that comprehension, during the short time of two weeks. But we are sure that the joint efforts of all the scientists involved has produced and will produce a measurable acceleration in the process. If this is true it will be a great satisfaction to us that this has happened in Brasil. The Southern Hemisphere in America has now begun to participate actively in the Astro nomical Society and for this, we are grateful to everyone who has helped.
Author: G.E.O. Giacaglia Publisher: Springer Science & Business Media ISBN: 9401033234 Category : Science Languages : en Pages : 540
Book Description
The subjects of resonance and stability are closely related to the problem of evolution of the solar system. It is a physically involving problem and the methods available to mathematics today seem unsatisfactory to produce pure non linear ways of attack. The linearization process in both subjects is clearly of doubtful significance, so that, even if very restrictive, numerical solutions are still the best and more valuable sources of informations. It is quite possible that we know now very little more of the entire problem that was known to Poincare, with the advantage that we can now compute much faster and with much more precision. We feel that the papers collected in this Symposium have contributed a step forward to the comprehension of Resonance, Periodic Orbits and Stability. In a field like this, it would be a surprise if one had gone a long way toward that comprehension, during the short time of two weeks. But we are sure that the joint efforts of all the scientists involved has produced and will produce a measurable acceleration in the process. If this is true it will be a great satisfaction to us that this has happened in Brasil. The Southern Hemisphere in America has now begun to participate actively in the Astro nomical Society and for this, we are grateful to everyone who has helped.
Author: Leigh Sneddon Publisher: ISBN: Category : Languages : en Pages : 38
Book Description
The linear stability analysis of a periodic orbit, X(o)(t), of a dynamical system X = F(X), is related to the anomalous ferromagnetic resonance properties of ferrites. It is shown to have a continuous sequence of normal mode problems associated with it. This sequence defines a natural set of coordinate axes which allow the stability analysis to be put in a form which has already been dealt with analytically in the ferrite resonance theory. A simplification which allowed the basic experimental properties to be accounted for is applied to the stability analysis. The simplified analytic solution is obtained for three-mode systems, its properties and consequences are discussed and it is checked against some rigorous results. (Author).
Author: Andre Deprit Publisher: ISBN: Category : Languages : en Pages : 16
Book Description
A bridge of periodic orbits consisting of a lane of stable orbits and a lane of unstable ones connects the two short period orbits around L sub 4 whose rotation number is equal to 12. (Author).
Author: Vladimir I. Arnol'd Publisher: Springer Science & Business Media ISBN: 3662025353 Category : Science Languages : en Pages : 305
Book Description
This work describes the fundamental principles, problems, and methods of elassical mechanics focussing on its mathematical aspects. The authors have striven to give an exposition stressing the working apparatus of elassical mechanics, rather than its physical foundations or applications. This appara tus is basically contained in Chapters 1, 3,4 and 5. Chapter 1 is devoted to the fundamental mathematical models which are usually employed to describe the motion of real mechanical systems. Special consideration is given to the study of motion under constraints, and also to problems concerned with the realization of constraints in dynamics. Chapter 3 is concerned with the symmetry groups of mechanical systems and the corresponding conservation laws. Also discussed are various aspects of the theory of the reduction of order for systems with symmetry, often used in applications. Chapter 4 contains abrief survey of various approaches to the problem of the integrability of the equations of motion, and discusses some of the most general and effective methods of integrating these equations. Various elassical examples of integrated problems are outlined. The material pre sen ted in this chapter is used in Chapter 5, which is devoted to one of the most fruitful branches of mechanics - perturbation theory. The main task of perturbation theory is the investigation of problems of mechanics which are" elose" to exact1y integrable problems.
Author: Alessandra Celletti Publisher: Springer Science & Business Media ISBN: 1402053258 Category : Science Languages : en Pages : 434
Book Description
The book provides the most recent advances of Celestial Mechanics, as provided by high-level scientists working in this field. It covers theoretical investigations as well as applications to concrete problems. Outstanding review papers are included in the book and they introduce the reader to leading subjects, like the variational approaches to find periodic orbits and the space debris polluting the circumterrestrial space.
Author: Sylvio Ferraz-Mello Publisher: Springer Science & Business Media ISBN: 9780792317821 Category : Science Languages : en Pages : 432
Book Description
This symposium was devoted to a new celestial mechanics whose aim has become the study of such `objects' as the planetary system, planetary rings, the asteroidal belt, meteor swarms, satellite systems, comet families, the zodiacal cloud, the preplanetary nebula, etc. When the three-body problem is considered instead of individual orbits we are, now, looking for the topology of extended regions of its phase space. This Symposium was one step in the effort to close the ties between two scientific families: the observationally-oriented scientists and the theoretically-oriented scientists.
Author: G.E.O. Giacaglia
Author: G.E.O. Giacaglia
Author: Giorgio E. O. Giacaglia
Author: 
Author: 
Author: G.E.O. Giacaglia
Author: Leigh Sneddon
Author: Andre Deprit
Author: Vladimir I. Arnol'd
Author: Alessandra Celletti
Author: Sylvio Ferraz-Mello