Classical and celestial mechanics : the Recife lectures /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Otros Autores: Cabral, Hildeberto, 1940-, Diacu, Florin, 1959-2018
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, N.J. ; Oxford : Princeton University Press, [2002]
Temas:
Many-body problem.
Celestial mechanics.
Mechanics.
Mechanics
Problème des N corps.
Mécanique céleste.
Mécanique.
mechanics (physics)
SCIENCE / Astronomy
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover Page
  • Half-title Page
  • Title Page
  • Copyright Page
  • Contents
  • Foreword
  • Preface
  • Central Configurations and Relative Equilibria for the JV-Body Problem
  • 1. Introduction
  • 2. Dziobek's Coordinates
  • 3. Configurations for the Three-Body Problem
  • 4. Configurations in the Four-Body Problem
  • 5. Configurations in the Five-Body Problem
  • 6. Palmore's Coordinates
  • Appendix A: The Area of a Triangle
  • Appendix B: Mathematica Code for the Four-Body Problem
  • Appendix C: Mathematica Code for the Planar Five-Body Problem
  • References
  • Singularities of the TV-Body Problem
  • 1. Introduction
  • 2. First Integrals
  • 3. Singularities
  • 4. Collisions
  • 5. Pseudocollisions
  • 6. Particular Cases
  • 7. Clustered Configurations
  • 8. Examples of Pseudocollisions
  • 9. Relationships between Singularities
  • 10. Extensions beyond Collision
  • 11. Block Regularization
  • 12. The Collision Manifold
  • 13. The Case
  • 14. The Case
  • 15. The Case
  • 16. Conclusions and Perspectives
  • References
  • Lectures on the Two-Body Problem
  • Introduction
  • Lecture 1. Preliminaries
  • Lecture 2. Two Solutions by Reduction
  • Lecture 3. Why Are Keplerian Orbits Closed?
  • Lecture 4. Concerning the Eccentricity Vector
  • Lecture 5. Lambert's Theorem
  • Bibliography and Author Index
  • Normal Forms of Hamiltonian Systems and Stability of Equilibria
  • 1. Introduction
  • 2. Hamiltonian Systems
  • 3. Symplectic Changes of Coordinates and Generating Functions
  • 4. Hamiltonian Flows
  • 5. Stability of Equilibria
  • 6. Normal Forms
  • 7. The Linear Normalization
  • 8. Some Stability Results
  • 9. The Restricted Three-Body Problem
  • 10. Deprit-Hori's Normalization Scheme.Proof of Theorem 6.1
  • References
  • Poincare's Compactification and Applications to Celestial Mechanics
  • 1. Introduction
  • 2. Poincare Compactification for Polynomial Vector Fields
  • 3. Poincare Compactincation for Polynomial Hamiltonian Vector Fields
  • 4. Generic Properties
  • 5. Behavior at Infinity in the Monomial Case
  • 6. The Kepler Problem
  • 6.1 The Kepler Problem on the Line
  • 6.2 The Kepler Problem in the Plane
  • 7. The Poincare Compactification for Homogeneous Functions
  • 8. The Kepler Problem without Regularization
  • 8.1 The Kepler Problem on the Line
  • 8.2 The Kepler Problem in the Plane
  • 9. Hill's Problem
  • References
  • The Motion of the Moon
  • 1. Remarks about the Accuracy of the Solution
  • 2. The Equations of Motion
  • 3. The Solution Method
  • 4. The Intermediate Orbit
  • 5. The Terms of First Order in the Inclination
  • 6. Terms at First Order in e
  • Appendix A: Canonical Transformation to Jacobi Coordinates
  • Appendix B: MACSYMA Program for the Intermediate Orbit
  • Appendix C: MACSYMA Program for Inclination
  • Appendix D: MACSYMA Program for First Order Terms in e
  • References
  • Lectures on Geometrical Methods in Mechanics

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