Description |
1 online resource (xviii, 385 pages :) illustrations |
Contents |
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 |
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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 |
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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 |
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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 |
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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 |
Bibliography |
Includes bibliographical references and index |
Subject |
Many-body problem.
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Celestial mechanics.
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Mechanics.
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Mechanics
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mechanics (physics)
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SCIENCE / Astronomy
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Mechanics
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Many-body problem
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Celestial mechanics
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Form |
Electronic book
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Author |
Cabral, Hildeberto, 1940-
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Diacu, Florin, 1959-2018.
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LC no. |
2002072263 |
ISBN |
0691050228 |
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9780691050225 |
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9780691222486 |
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0691222487 |
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