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The integral manifolds of the three body problem / / Christopher K. McCord, Kenneth R. Meyer, Quidong Wang
| The integral manifolds of the three body problem / / Christopher K. McCord, Kenneth R. Meyer, Quidong Wang |
| Autore | McCord Christopher Keil |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1998 |
| Descrizione fisica | 1 online resource (106 p.) |
| Disciplina | 521 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Three-body problem
Celestial mechanics Manifolds (Mathematics) |
| ISBN | 1-4704-0217-3 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""1. The integrals and manifolds""; ""2. History of the problem""; ""3. Summary of results ""; ""Chapter 2. The Decomposition of the Spaces""; ""1. The spaces and maps""; ""2. The geometry of the sets""; ""Chapter 3. The Cohomology""; ""1. The cohomology of k[sub(R)](c,h)""; ""2. The cohomology of k(c,h)""; ""3. The homeomorphism type of h(c,h) and h[sub(R)](c,h)""; ""4. The cohomology of m[sub(R)](c,h)""; ""5. The cohomology of m(c,h)""; ""Chapter 4. The analysis of k(c,h) for equal masses""
""1. y[sub(1)][sup(2)] + y[sub(2)][sup(2)] as function of Ï?,Ï? for equal masses""""2. The semi-minor axis of the ellipse for equal masses""; ""3. The graphs of Z = f(X) and Z = g(X) for equal masses""; ""4. The semi- major axis of the ellipse for equal masses""; ""5. The feasible region c(c, h)""; ""6. k[sub(R)](c,h) for equal masses""; ""7. Orientation in k(c,h)""; ""8. Positive energy""; ""Chapter 5. The analysis of k(c,h) for general masses""; ""1. y[sub(1)][sup(2)] + y[sub(2)][sup(2)] as function of Ï?,Ï? for general masses""; ""2. The semi-minor axis of the ellipse"" ""3. The graph of Z = f(X) and Z = g(X) for general masses""""4. The semi-major axis of the ellipse for unequal masses""; ""5. k[sub(R)](c,h) for unequal masses""; ""Bibliography"" |
| Record Nr. | UNINA-9910820698503321 |
McCord Christopher Keil
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1998 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An introduction to celestial mechanics / / Richard Fitzpatrick [[electronic resource]]
| An introduction to celestial mechanics / / Richard Fitzpatrick [[electronic resource]] |
| Autore | Fitzpatrick Richard <1963-> |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2012 |
| Descrizione fisica | 1 online resource (x, 266 pages) : digital, PDF file(s) |
| Disciplina | 521 |
| Soggetto topico | Celestial mechanics |
| ISBN |
1-107-23960-5
1-107-23190-6 1-280-77519-X 9786613685582 1-139-51800-3 1-139-51542-X 1-139-15231-9 1-139-51707-4 1-139-51450-4 1-139-51893-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; An Introduction to Celestial Mechanics; Title; Copyright; Contents; Preface; 1: Newtonian mechanics; 1.1 Introduction; 1.2 Newton's laws of motion; 1.3 Newton's first law of motion; 1.4 Newton's second law of motion; 1.5 Newton's third law of motion; 1.6 Nonisolated systems; 1.7 Motion in one-dimensional potential; 1.8 Simple harmonic motion; 1.9 Two-body problem; Exercises; 2: Newtonian gravity; 2.1 Introduction; 2.2 Gravitational potential; 2.3 Gravitational potential energy; 2.4 Axially symmetric mass distributions; 2.5 Potential due to a uniform sphere
2.6 Potential outside a uniform spheroid2.7 Potential due to a uniform ring; Exercises; 3: Keplerian orbits; 3.1 Introduction; 3.2 Kepler's laws; 3.3 Conservation laws; 3.4 Plane polar coordinates; 3.5 Kepler's second law; 3.6 Kepler's first law; 3.7 Kepler's third law; 3.8 Orbital parameters; 3.9 Orbital energies; 3.10 Transfer orbits; 3.11 Elliptical orbits; 3.12 Orbital elements; 3.13 Planetary orbits; 3.14 Parabolic orbits; 3.15 Hyperbolic orbits; 3.16 Binary star systems; Exercises; 4: Orbits in central force fields; 4.1 Introduction; 4.2 Motion in a general central force field 4.3 Motion in a nearly circular orbit4.4 Perihelion precession of planets; 4.5 Perihelion precession of Mercury; Exercises; 5: Rotating reference frames; 5.1 Introduction; 5.2 Rotating reference frames; 5.3 Centrifugal acceleration; 5.4 Coriolis force; 5.5 Rotational flattening; 5.6 Tidal elongation; 5.7 Tidal torques; 5.8 Roche radius; Exercises; 6 Lagrangian mechanics; 6.1 Introduction; 6.2 Generalized coordinates; 6.3 Generalized forces; 6.4 Lagrange's equation; 6.5 Generalized momenta; Exercises; 7: Rigid body rotation; 7.1 Introduction; 7.2 Fundamental equations 7.3 Moment of inertia tensor7.4 Rotational kinetic energy; 7.5 Principal axes of rotation; 7.6 Euler's equations; 7.7 Euler angles; 7.8 Free precession of the Earth; 7.9 MacCullagh's formula; 7.10 Forced precession and nutation of the Earth; 7.11 Spin-orbit coupling; 7.12 Cassini's laws; Exercises; 8: Three-body problem; 8.1 Introduction; 8.2 Circular restricted three-body problem; 8.3 Jacobi integral; 8.4 Tisserand criterion; 8.5 Co-rotating frame; 8.6 Lagrange points; 8.7 Zero-velocity surfaces; 8.8 Stability of Lagrange points; Exercises; 9: Secular perturbation theory; 9.1 Introduction 9.2 Evolution equations for a two-planet solar system9.3 Secular evolution of planetary orbits; 9.4 Secular evolution of asteroid orbits; 9.5 Secular evolution of artificial satellite orbits; Exercises; 10: Lunar motion; 10.1 Introduction; 10.2 Preliminary analysis; 10.3 Lunar equations of motion; 10.4 Unperturbed lunar motion; 10.5 Perturbed lunar motion; 10.6 Description of lunar motion; Exercises; Appendix A: Useful mathematics; A.1 Calculus; A.2 Series expansions; A.3 Trigonometric identities; A.4 Vector identities; A.5 Conservative fields; A.6 Rotational coordinate transformations A.7 Precession |
| Record Nr. | UNINA-9910462429803321 |
|
Fitzpatrick Richard <1963->
|
||
| Cambridge : , : Cambridge University Press, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An introduction to celestial mechanics / / Richard Fitzpatrick [[electronic resource]]
| An introduction to celestial mechanics / / Richard Fitzpatrick [[electronic resource]] |
| Autore | Fitzpatrick Richard <1963-> |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2012 |
| Descrizione fisica | 1 online resource (x, 266 pages) : digital, PDF file(s) |
| Disciplina | 521 |
| Soggetto topico | Celestial mechanics |
| ISBN |
1-107-23960-5
1-107-23190-6 1-280-77519-X 9786613685582 1-139-51800-3 1-139-51542-X 1-139-15231-9 1-139-51707-4 1-139-51450-4 1-139-51893-3 |
| Classificazione | SCI005000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; An Introduction to Celestial Mechanics; Title; Copyright; Contents; Preface; 1: Newtonian mechanics; 1.1 Introduction; 1.2 Newton's laws of motion; 1.3 Newton's first law of motion; 1.4 Newton's second law of motion; 1.5 Newton's third law of motion; 1.6 Nonisolated systems; 1.7 Motion in one-dimensional potential; 1.8 Simple harmonic motion; 1.9 Two-body problem; Exercises; 2: Newtonian gravity; 2.1 Introduction; 2.2 Gravitational potential; 2.3 Gravitational potential energy; 2.4 Axially symmetric mass distributions; 2.5 Potential due to a uniform sphere
2.6 Potential outside a uniform spheroid2.7 Potential due to a uniform ring; Exercises; 3: Keplerian orbits; 3.1 Introduction; 3.2 Kepler's laws; 3.3 Conservation laws; 3.4 Plane polar coordinates; 3.5 Kepler's second law; 3.6 Kepler's first law; 3.7 Kepler's third law; 3.8 Orbital parameters; 3.9 Orbital energies; 3.10 Transfer orbits; 3.11 Elliptical orbits; 3.12 Orbital elements; 3.13 Planetary orbits; 3.14 Parabolic orbits; 3.15 Hyperbolic orbits; 3.16 Binary star systems; Exercises; 4: Orbits in central force fields; 4.1 Introduction; 4.2 Motion in a general central force field 4.3 Motion in a nearly circular orbit4.4 Perihelion precession of planets; 4.5 Perihelion precession of Mercury; Exercises; 5: Rotating reference frames; 5.1 Introduction; 5.2 Rotating reference frames; 5.3 Centrifugal acceleration; 5.4 Coriolis force; 5.5 Rotational flattening; 5.6 Tidal elongation; 5.7 Tidal torques; 5.8 Roche radius; Exercises; 6 Lagrangian mechanics; 6.1 Introduction; 6.2 Generalized coordinates; 6.3 Generalized forces; 6.4 Lagrange's equation; 6.5 Generalized momenta; Exercises; 7: Rigid body rotation; 7.1 Introduction; 7.2 Fundamental equations 7.3 Moment of inertia tensor7.4 Rotational kinetic energy; 7.5 Principal axes of rotation; 7.6 Euler's equations; 7.7 Euler angles; 7.8 Free precession of the Earth; 7.9 MacCullagh's formula; 7.10 Forced precession and nutation of the Earth; 7.11 Spin-orbit coupling; 7.12 Cassini's laws; Exercises; 8: Three-body problem; 8.1 Introduction; 8.2 Circular restricted three-body problem; 8.3 Jacobi integral; 8.4 Tisserand criterion; 8.5 Co-rotating frame; 8.6 Lagrange points; 8.7 Zero-velocity surfaces; 8.8 Stability of Lagrange points; Exercises; 9: Secular perturbation theory; 9.1 Introduction 9.2 Evolution equations for a two-planet solar system9.3 Secular evolution of planetary orbits; 9.4 Secular evolution of asteroid orbits; 9.5 Secular evolution of artificial satellite orbits; Exercises; 10: Lunar motion; 10.1 Introduction; 10.2 Preliminary analysis; 10.3 Lunar equations of motion; 10.4 Unperturbed lunar motion; 10.5 Perturbed lunar motion; 10.6 Description of lunar motion; Exercises; Appendix A: Useful mathematics; A.1 Calculus; A.2 Series expansions; A.3 Trigonometric identities; A.4 Vector identities; A.5 Conservative fields; A.6 Rotational coordinate transformations A.7 Precession |
| Record Nr. | UNINA-9910790346103321 |
|
Fitzpatrick Richard <1963->
|
||
| Cambridge : , : Cambridge University Press, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An introduction to celestial mechanics / / Richard Fitzpatrick [[electronic resource]]
| An introduction to celestial mechanics / / Richard Fitzpatrick [[electronic resource]] |
| Autore | Fitzpatrick Richard <1963-> |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2012 |
| Descrizione fisica | 1 online resource (x, 266 pages) : digital, PDF file(s) |
| Disciplina | 521 |
| Soggetto topico | Celestial mechanics |
| ISBN |
1-107-23960-5
1-107-23190-6 1-280-77519-X 9786613685582 1-139-51800-3 1-139-51542-X 1-139-15231-9 1-139-51707-4 1-139-51450-4 1-139-51893-3 |
| Classificazione | SCI005000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; An Introduction to Celestial Mechanics; Title; Copyright; Contents; Preface; 1: Newtonian mechanics; 1.1 Introduction; 1.2 Newton's laws of motion; 1.3 Newton's first law of motion; 1.4 Newton's second law of motion; 1.5 Newton's third law of motion; 1.6 Nonisolated systems; 1.7 Motion in one-dimensional potential; 1.8 Simple harmonic motion; 1.9 Two-body problem; Exercises; 2: Newtonian gravity; 2.1 Introduction; 2.2 Gravitational potential; 2.3 Gravitational potential energy; 2.4 Axially symmetric mass distributions; 2.5 Potential due to a uniform sphere
2.6 Potential outside a uniform spheroid2.7 Potential due to a uniform ring; Exercises; 3: Keplerian orbits; 3.1 Introduction; 3.2 Kepler's laws; 3.3 Conservation laws; 3.4 Plane polar coordinates; 3.5 Kepler's second law; 3.6 Kepler's first law; 3.7 Kepler's third law; 3.8 Orbital parameters; 3.9 Orbital energies; 3.10 Transfer orbits; 3.11 Elliptical orbits; 3.12 Orbital elements; 3.13 Planetary orbits; 3.14 Parabolic orbits; 3.15 Hyperbolic orbits; 3.16 Binary star systems; Exercises; 4: Orbits in central force fields; 4.1 Introduction; 4.2 Motion in a general central force field 4.3 Motion in a nearly circular orbit4.4 Perihelion precession of planets; 4.5 Perihelion precession of Mercury; Exercises; 5: Rotating reference frames; 5.1 Introduction; 5.2 Rotating reference frames; 5.3 Centrifugal acceleration; 5.4 Coriolis force; 5.5 Rotational flattening; 5.6 Tidal elongation; 5.7 Tidal torques; 5.8 Roche radius; Exercises; 6 Lagrangian mechanics; 6.1 Introduction; 6.2 Generalized coordinates; 6.3 Generalized forces; 6.4 Lagrange's equation; 6.5 Generalized momenta; Exercises; 7: Rigid body rotation; 7.1 Introduction; 7.2 Fundamental equations 7.3 Moment of inertia tensor7.4 Rotational kinetic energy; 7.5 Principal axes of rotation; 7.6 Euler's equations; 7.7 Euler angles; 7.8 Free precession of the Earth; 7.9 MacCullagh's formula; 7.10 Forced precession and nutation of the Earth; 7.11 Spin-orbit coupling; 7.12 Cassini's laws; Exercises; 8: Three-body problem; 8.1 Introduction; 8.2 Circular restricted three-body problem; 8.3 Jacobi integral; 8.4 Tisserand criterion; 8.5 Co-rotating frame; 8.6 Lagrange points; 8.7 Zero-velocity surfaces; 8.8 Stability of Lagrange points; Exercises; 9: Secular perturbation theory; 9.1 Introduction 9.2 Evolution equations for a two-planet solar system9.3 Secular evolution of planetary orbits; 9.4 Secular evolution of asteroid orbits; 9.5 Secular evolution of artificial satellite orbits; Exercises; 10: Lunar motion; 10.1 Introduction; 10.2 Preliminary analysis; 10.3 Lunar equations of motion; 10.4 Unperturbed lunar motion; 10.5 Perturbed lunar motion; 10.6 Description of lunar motion; Exercises; Appendix A: Useful mathematics; A.1 Calculus; A.2 Series expansions; A.3 Trigonometric identities; A.4 Vector identities; A.5 Conservative fields; A.6 Rotational coordinate transformations A.7 Precession |
| Record Nr. | UNINA-9910814785103321 |
|
Fitzpatrick Richard <1963->
|
||
| Cambridge : , : Cambridge University Press, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An introduction to celestial mechanics / Theodore E. Sterne
| An introduction to celestial mechanics / Theodore E. Sterne |
| Autore | Sterne, Theodore E. |
| Pubbl/distr/stampa | New York : Interscience Publishers, 1960 |
| Descrizione fisica | 206 p. : ill. ; 21 cm. |
| Collana | Interscience tracts on physics and astronomy ; 9 |
| Soggetto topico | Celestial mechanics |
| Classificazione |
53.1.3
521.1 QB351.S75 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001017209707536 |
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Sterne, Theodore E.
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| New York : Interscience Publishers, 1960 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Introduction to the Maths and Physics of the Solar System / / Lucio Piccirillo
| Introduction to the Maths and Physics of the Solar System / / Lucio Piccirillo |
| Autore | Piccirillo Lucio |
| Edizione | [First edition.] |
| Pubbl/distr/stampa | Boca Raton, FL : , : CRC Press, , [2020] |
| Descrizione fisica | 1 online resource (238 pages) |
| Disciplina | 521 |
| Soggetto topico | Celestial mechanics |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910795122703321 |
|
Piccirillo Lucio
|
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| Boca Raton, FL : , : CRC Press, , [2020] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to the Maths and Physics of the Solar System / / Lucio Piccirillo
| Introduction to the Maths and Physics of the Solar System / / Lucio Piccirillo |
| Autore | Piccirillo Lucio |
| Edizione | [First edition.] |
| Pubbl/distr/stampa | Boca Raton, FL : , : CRC Press, , [2020] |
| Descrizione fisica | 1 online resource (238 pages) |
| Disciplina | 521 |
| Soggetto topico | Celestial mechanics |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910825612303321 |
|
Piccirillo Lucio
|
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| Boca Raton, FL : , : CRC Press, , [2020] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
KAM stability and celestial mechanics / / Alessandra Celletti, Luigi Chierchia
| KAM stability and celestial mechanics / / Alessandra Celletti, Luigi Chierchia |
| Autore | Celletti A (Alessandra) |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2007 |
| Descrizione fisica | 1 online resource (150 p.) |
| Disciplina | 521 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Three-body problem
Celestial mechanics Perturbation (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0482-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""1.1. Quasi-periodic solutions for the n-body problem""; ""1.2. A stability theorem for the Sun-Jupiter-Victoria system viewed as a restricted, circular, planar three-body problem""; ""1.3. About the proof of the Sun-Jupiter-Victoria stability theorem""; ""1.4. A short history of KAM stability estimates""; ""1.5. A section-by-section summary""; ""Chapter 2. Iso-energetic KAM Theory""; ""2.1. Notations""; ""2.2. KAM tori""; ""2.3. Newton scheme for finding iso-energetic KAM tori""; ""2.4. The KAM Map""; ""2.5. Technical Tools""
""2.6. The KAM Norm Map""""2.7. Iso-energetic KAM Theorem""; ""2.8. Iso-energetic Lindstedt series""; ""Chapter 3. The Restricted, Circular, Planar Three-body Problem""; ""3.1. The restricted three-body problem""; ""3.2. Delaunay action-angle variables for the two-body problem""; ""3.3. The restricted, circular, planar three-body problem viewed as nearly-integrable Hamiltonian system""; ""3.4. The Sun-Jupiter-Asteroid problem""; ""Chapter 4. KAM Stability of the Sun-Jupiter-Victoria Problem"" ""4.1. Iso-energetic Lindstedt series for the Sun-Jupiter-Asteroid problem and choice of the initial approximate tori (u[sup((0)±)], v[sup((0)±)], w[sup((0)±)])""""4.2. Evaluation of the input parameters of the KAM norm map associated to the approximate tori (u[sup((0)±)], v[sup((0)±)], w[sup((0)±)])""; ""4.3. Iterations of the KAM map""; ""4.4. Application of the iso-energetic KAM theorem and perpetual stability of the Sun-Jupiter-Victoria problem""; ""Appendix A. The Ellipse""; ""Appendix B. Diophantine Estimates""; ""B.1. Diophantine estimates for special quadratic numbers"" ""B.2. Estimates on s[sub(p)],k(Î?)""""Appendix C. Interval Arithmetic""; ""Appendix D. A Guide to the Computer Programs""; ""Bibliography"" |
| Record Nr. | UNINA-9910480507803321 |
|
Celletti A (Alessandra)
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
KAM stability and celestial mechanics / / Alessandra Celletti, Luigi Chierchia
| KAM stability and celestial mechanics / / Alessandra Celletti, Luigi Chierchia |
| Autore | Celletti A (Alessandra) |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2007 |
| Descrizione fisica | 1 online resource (150 p.) |
| Disciplina | 521 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Three-body problem
Celestial mechanics Perturbation (Mathematics) |
| ISBN | 1-4704-0482-6 |
| Classificazione |
39.23
31.81 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""1.1. Quasi-periodic solutions for the n-body problem""; ""1.2. A stability theorem for the Sun-Jupiter-Victoria system viewed as a restricted, circular, planar three-body problem""; ""1.3. About the proof of the Sun-Jupiter-Victoria stability theorem""; ""1.4. A short history of KAM stability estimates""; ""1.5. A section-by-section summary""; ""Chapter 2. Iso-energetic KAM Theory""; ""2.1. Notations""; ""2.2. KAM tori""; ""2.3. Newton scheme for finding iso-energetic KAM tori""; ""2.4. The KAM Map""; ""2.5. Technical Tools""
""2.6. The KAM Norm Map""""2.7. Iso-energetic KAM Theorem""; ""2.8. Iso-energetic Lindstedt series""; ""Chapter 3. The Restricted, Circular, Planar Three-body Problem""; ""3.1. The restricted three-body problem""; ""3.2. Delaunay action-angle variables for the two-body problem""; ""3.3. The restricted, circular, planar three-body problem viewed as nearly-integrable Hamiltonian system""; ""3.4. The Sun-Jupiter-Asteroid problem""; ""Chapter 4. KAM Stability of the Sun-Jupiter-Victoria Problem"" ""4.1. Iso-energetic Lindstedt series for the Sun-Jupiter-Asteroid problem and choice of the initial approximate tori (u[sup((0)±)], v[sup((0)±)], w[sup((0)±)])""""4.2. Evaluation of the input parameters of the KAM norm map associated to the approximate tori (u[sup((0)±)], v[sup((0)±)], w[sup((0)±)])""; ""4.3. Iterations of the KAM map""; ""4.4. Application of the iso-energetic KAM theorem and perpetual stability of the Sun-Jupiter-Victoria problem""; ""Appendix A. The Ellipse""; ""Appendix B. Diophantine Estimates""; ""B.1. Diophantine estimates for special quadratic numbers"" ""B.2. Estimates on s[sub(p)],k(Î?)""""Appendix C. Interval Arithmetic""; ""Appendix D. A Guide to the Computer Programs""; ""Bibliography"" |
| Record Nr. | UNINA-9910788744103321 |
|
Celletti A (Alessandra)
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
KAM stability and celestial mechanics / / Alessandra Celletti, Luigi Chierchia
| KAM stability and celestial mechanics / / Alessandra Celletti, Luigi Chierchia |
| Autore | Celletti A (Alessandra) |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2007 |
| Descrizione fisica | 1 online resource (150 p.) |
| Disciplina | 521 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Three-body problem
Celestial mechanics Perturbation (Mathematics) |
| ISBN | 1-4704-0482-6 |
| Classificazione |
39.23
31.81 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""1.1. Quasi-periodic solutions for the n-body problem""; ""1.2. A stability theorem for the Sun-Jupiter-Victoria system viewed as a restricted, circular, planar three-body problem""; ""1.3. About the proof of the Sun-Jupiter-Victoria stability theorem""; ""1.4. A short history of KAM stability estimates""; ""1.5. A section-by-section summary""; ""Chapter 2. Iso-energetic KAM Theory""; ""2.1. Notations""; ""2.2. KAM tori""; ""2.3. Newton scheme for finding iso-energetic KAM tori""; ""2.4. The KAM Map""; ""2.5. Technical Tools""
""2.6. The KAM Norm Map""""2.7. Iso-energetic KAM Theorem""; ""2.8. Iso-energetic Lindstedt series""; ""Chapter 3. The Restricted, Circular, Planar Three-body Problem""; ""3.1. The restricted three-body problem""; ""3.2. Delaunay action-angle variables for the two-body problem""; ""3.3. The restricted, circular, planar three-body problem viewed as nearly-integrable Hamiltonian system""; ""3.4. The Sun-Jupiter-Asteroid problem""; ""Chapter 4. KAM Stability of the Sun-Jupiter-Victoria Problem"" ""4.1. Iso-energetic Lindstedt series for the Sun-Jupiter-Asteroid problem and choice of the initial approximate tori (u[sup((0)±)], v[sup((0)±)], w[sup((0)±)])""""4.2. Evaluation of the input parameters of the KAM norm map associated to the approximate tori (u[sup((0)±)], v[sup((0)±)], w[sup((0)±)])""; ""4.3. Iterations of the KAM map""; ""4.4. Application of the iso-energetic KAM theorem and perpetual stability of the Sun-Jupiter-Victoria problem""; ""Appendix A. The Ellipse""; ""Appendix B. Diophantine Estimates""; ""B.1. Diophantine estimates for special quadratic numbers"" ""B.2. Estimates on s[sub(p)],k(Î?)""""Appendix C. Interval Arithmetic""; ""Appendix D. A Guide to the Computer Programs""; ""Bibliography"" |
| Record Nr. | UNINA-9910827760803321 |
|
Celletti A (Alessandra)
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
