The Restricted 3-Body Problem: Plane Periodic Orbits
Restricted 3-Body Problem: Plane Periodic Orbits
1st Edition
Published on 3. May 2011
XIV, 362 pages
978-3-11-090173-3 (ISBN)
Description
No detailed description available for "The Restricted 3-Body Problem: Plane Periodic Orbits".
Reviews / Votes
"This beautiful book is written by a prominent specialist in the qualitative theory of ordinary differential equations, especially the theory of Hamiltonian systems and applications to celestial mechanics. Although devoted mainly to the restricted 3-body problem (R3BP), it can serve as a perfect model of how such qualitative methods can be applied in the study of a classical problem of mechanics. The book will undoubtedly become a reference source for people interested in the topics mentioned above [...]." Mathematical Reviews (review of the original Russian edition)
More details
Series
Edition
Reprint 2011
Language
English
Place of publication
Berlin/Boston
Germany
Target group
Professional and scholarly
US School Grade: College Graduate Student
Illustrations
12 s/w Tabellen, 93 Abbildungen
93 ill., 12 tbl.
File size
83,25 MB
ISBN-13
978-3-11-090173-3 (9783110901733)
Schweitzer Classification
Other editions
Additional editions
Alexander D. Bruno
The Restricted 3-Body Problem: Plane Periodic Orbits
Book
09/1994
1st Edition
De Gruyter
€210.00
Shipment within 7-9 days
Alexander D. Bruno
The Restricted 3-Body Problem: Plane Periodic Orbits
Book
01/1994
1st Edition
De Gruyter
€299.00
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Content
- Intro
- Preface
- Basic notation
- Introduction
- Part I. Mathematical means
- Chapter I. The normal form of a Hamiltonian system
- 1 The normal form of a linear system
- 2 Nonlinear normalization
- 3 Lowering the number of degrees of freedom
- 4 Periodic and conditionally-periodic solutions
- 5 Generalizations
- 6 Notes
- Chapter II. Normalization of a Hamiltonian system near a cycle or a torus
- 1 The normal form of a linear Hamiltonian system with periodic coefficients
- 2 The normal form in a neighbourhood of a periodic solution
- 3 The neighbourhood of an invariant torus
- 4 A system with two degrees of freedom
- 5 Notes
- Part II. Solutions of the limiting problem (µ = 0)
- Chapter III. Periodic solutions and arc solutions
- 1 Formulation of the restricted three-body problem
- 2 The two-body problem
- 3 The restricted three-body problem for µ = 0
- 4 Notes
- Chapter IV. Properties of arc solutions of the families S and TN
- 1 Orbits of the families S
- 2 The structure of the set of characteristics of the families S and TN
- 3 Values of the Jacobian constant
- 4 Notes
- Chapter V. Extrema of the Hamiltonian function on families of arc solutions
- 1 The function G
- 2 Partial derivatives of the function G
- 3 Classification of the segments of the characteristics
- 4 Estimation of the number of intersections of a segment of a characteristic with a level line of the function G
- 5 The domain ?3
- 6 Conclusion
- Chapter VI. Trajectories of collisions
- 1 The problem of two bodies P1 and P3
- 2 Trajectories of collision with P2
- 3 Arc solutions with consecutive collisions
- 4 Isolation of critical solutions
- 5 Notes
- Part III. Regular generating solutions
- Chapter VII. Solutions of the second kind
- 1 Sets of periodic solutions
- 2 The restricted three-body problem
- 3 Averaging of the perturbing function
- 4 Computation of generating families
- 5 Concerning the programs
- 6 Other properties of the families EN
- 7 Limits of generating families
- 8 Conditionally-periodic solutions of the second kind
- 9 Notes
- Chapter VIII. Solutions of the first kind
- 1 Reduction to the normal form
- 2 Integration of the normal form for rational ? = p~~/q~~
- 3 Application to the restricted problem
- 4 Conclusion
- 5 The neighbourhood of stationary points
- 6 Notes
- Chapter IX. Generating arc solutions from C¯1C¯1
- 1 Generating solutions of collisions with P1
- 2 Computation of families of generating arc solutions
- 3 Asymptotics of families of generating arc solutions
- 4 Concerning periodic solutions with collisions
- 5 Notes
- Chapter X. Perturbations of hyperbolic orbits
- 1 The normal form
- 2 Application to the restricted problem
- 3 Notes
- Appendix. Tables of generating families and their perturbations
- Bibliography
- Author index
- Subject index
