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Celestial dynamics [[electronic resource] ] : chaoticity and dynamics of celestial systems / / Rudolf Dvorak and Christoph Lhotka
| Celestial dynamics [[electronic resource] ] : chaoticity and dynamics of celestial systems / / Rudolf Dvorak and Christoph Lhotka |
| Autore | Dvorak R |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Weinheim, Germany, : Wiley-VCH Verlag GmbH & Co. KGaA, 2013 |
| Descrizione fisica | 1 online resource (323 p.) |
| Disciplina | 521 |
| Altri autori (Persone) | LhotkaChristoph |
| Soggetto topico |
Celestial mechanics
Differentiable dynamical systems |
| ISBN |
3-527-65187-X
3-527-65185-3 3-527-65188-8 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Celestial Dynamics; Contents; Preface; 1 Introduction: the Challenge of Science; 2 Hamiltonian Mechanics; 2.1 Hamilton's Equations from Hamiltonian Principle; 2.2 Poisson Brackets; 2.3 Canonical Transformations; 2.4 Hamilton-Jacobi Theory; 2.5 Action-Angle Variables; 3 Numerical and Analytical Tools; 3.1 Mappings; 3.1.1 Simple Examples; 3.1.2 Hadjidemetriou Mapping; 3.2 Lie-Series Numerical Integration; 3.2.1 A Simple Example; 3.3 Chaos Indicators; 3.3.1 Lyapunov Characteristic Exponent; 3.3.2 Fast Lyapunov Indicator; 3.3.3 Mean Exponential Growth Factor of Nearby Orbits
3.3.4 Smaller Alignment Index 3.3.5 Spectral Analysis Method; 3.4 Perturbation Theory; 3.4.1 Lie-Transformation Method; 3.4.2 Mapping method; 4 The Stability Problem; 4.1 Review on Different Concepts of Stability; 4.2 Integrable Systems; 4.3 Nearly Integrable Systems; 4.4 Resonance Dynamics; 4.5 KAM Theorem; 4.6 Nekhoroshev Theorem; 4.7 The Froeschlé-Guzzo-Lega Hamiltonian; 5 The Two-Body Problem; 5.1 From Newton to Kepler; 5.2 Unperturbed Kepler Motion; 5.3 Classification of Orbits: Ellipses, Hyperbolae and Parabolae; 5.4 Kepler Equation; 5.5 Complex Description; 5.5.1 The KS-Transformation 5.6 Motion in Space and the Keplerian Elements 5.7 Astronomical Determination of the Gravitational Constant; 5.8 Solution of the Kepler Equation; 6 The Restricted Three-Body Problem; 6.1 Set-Up and Formulation; 6.2 Equilibria of the System; 6.3 Motion Close to L4 and L5; 6.4 Motion Close to L1, L2, L3; 6.5 Potential and the Zero Velocity Curves; 6.6 Spatial Restricted Three-Body Problem; 6.7 Tisserand Criterion; 6.8 Elliptic Restricted Three-Body Problem; 6.9 Dissipative Restricted Three-Body Problem; 7 The Sitnikov Problem; 7.1 Circular Case: the MacMillan Problem; 7.1.1 Qualitative Estimates 7.2 Motion of the Planet off the z-Axes 7.3 Elliptic Case; 7.3.1 Numerical Results; 7.3.2 Analytical Results; 7.4 The Vrabec Mapping; 7.5 General Sitnikov Problem; 7.5.1 Qualitative Estimates; 7.5.2 Phase Space Structure; 8 Planetary Theory; 8.1 Planetary Perturbation Theory; 8.1.1 A Simple Example; 8.1.2 Principles of Planetary Theory; 8.1.3 The Integration Constants - the Osculating Elements; 8.1.4 First-Order Perturbation; 8.1.5 Second-Order Perturbation; 8.2 Equations of Motion for n Bodies; 8.2.1 The Virial Theorem; 8.2.2 Reduction to Heliocentric Coordinates 8.3 Lagrange Equations of the Planetary n-Body Problem 8.3.1 Legendre Polynomials; 8.3.2 Delaunay Elements; 8.4 The Perturbing Function in Elliptic Orbital Elements; 8.5 Explicit First-Order Planetary Theory for the Osculating Elements; 8.5.1 Perturbation of the Mean Longitude; 8.6 Small Divisors; 8.7 Long-Term Evolution of Our Planetary System; 9 Resonances; 9.1 Mean Motion Resonances in Our Planetary System; 9.1.1 The 13:8 Resonance between Venus and Earth; 9.1.2 The 1:1 Mean Motion Resonance: Trojan Asteroids; 9.2 Method of Laplace-Lagrange; 9.3 Secular Resonances 9.3.1 Asteroids with Small Inclinations and Eccentricities |
| Record Nr. | UNINA-9910139041003321 |
Dvorak R
|
||
| Weinheim, Germany, : Wiley-VCH Verlag GmbH & Co. KGaA, 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Celestial dynamics : chaoticity and dynamics of celestial systems / / Rudolf Dvorak and Christoph Lhotka
| Celestial dynamics : chaoticity and dynamics of celestial systems / / Rudolf Dvorak and Christoph Lhotka |
| Autore | Dvorak R |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Weinheim, Germany, : Wiley-VCH Verlag GmbH & Co. KGaA, 2013 |
| Descrizione fisica | 1 online resource (323 p.) |
| Disciplina | 521 |
| Altri autori (Persone) | LhotkaChristoph |
| Soggetto topico |
Celestial mechanics
Differentiable dynamical systems |
| ISBN |
3-527-65187-X
3-527-65185-3 3-527-65188-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Celestial Dynamics; Contents; Preface; 1 Introduction: the Challenge of Science; 2 Hamiltonian Mechanics; 2.1 Hamilton's Equations from Hamiltonian Principle; 2.2 Poisson Brackets; 2.3 Canonical Transformations; 2.4 Hamilton-Jacobi Theory; 2.5 Action-Angle Variables; 3 Numerical and Analytical Tools; 3.1 Mappings; 3.1.1 Simple Examples; 3.1.2 Hadjidemetriou Mapping; 3.2 Lie-Series Numerical Integration; 3.2.1 A Simple Example; 3.3 Chaos Indicators; 3.3.1 Lyapunov Characteristic Exponent; 3.3.2 Fast Lyapunov Indicator; 3.3.3 Mean Exponential Growth Factor of Nearby Orbits
3.3.4 Smaller Alignment Index 3.3.5 Spectral Analysis Method; 3.4 Perturbation Theory; 3.4.1 Lie-Transformation Method; 3.4.2 Mapping method; 4 The Stability Problem; 4.1 Review on Different Concepts of Stability; 4.2 Integrable Systems; 4.3 Nearly Integrable Systems; 4.4 Resonance Dynamics; 4.5 KAM Theorem; 4.6 Nekhoroshev Theorem; 4.7 The Froeschlé-Guzzo-Lega Hamiltonian; 5 The Two-Body Problem; 5.1 From Newton to Kepler; 5.2 Unperturbed Kepler Motion; 5.3 Classification of Orbits: Ellipses, Hyperbolae and Parabolae; 5.4 Kepler Equation; 5.5 Complex Description; 5.5.1 The KS-Transformation 5.6 Motion in Space and the Keplerian Elements 5.7 Astronomical Determination of the Gravitational Constant; 5.8 Solution of the Kepler Equation; 6 The Restricted Three-Body Problem; 6.1 Set-Up and Formulation; 6.2 Equilibria of the System; 6.3 Motion Close to L4 and L5; 6.4 Motion Close to L1, L2, L3; 6.5 Potential and the Zero Velocity Curves; 6.6 Spatial Restricted Three-Body Problem; 6.7 Tisserand Criterion; 6.8 Elliptic Restricted Three-Body Problem; 6.9 Dissipative Restricted Three-Body Problem; 7 The Sitnikov Problem; 7.1 Circular Case: the MacMillan Problem; 7.1.1 Qualitative Estimates 7.2 Motion of the Planet off the z-Axes 7.3 Elliptic Case; 7.3.1 Numerical Results; 7.3.2 Analytical Results; 7.4 The Vrabec Mapping; 7.5 General Sitnikov Problem; 7.5.1 Qualitative Estimates; 7.5.2 Phase Space Structure; 8 Planetary Theory; 8.1 Planetary Perturbation Theory; 8.1.1 A Simple Example; 8.1.2 Principles of Planetary Theory; 8.1.3 The Integration Constants - the Osculating Elements; 8.1.4 First-Order Perturbation; 8.1.5 Second-Order Perturbation; 8.2 Equations of Motion for n Bodies; 8.2.1 The Virial Theorem; 8.2.2 Reduction to Heliocentric Coordinates 8.3 Lagrange Equations of the Planetary n-Body Problem 8.3.1 Legendre Polynomials; 8.3.2 Delaunay Elements; 8.4 The Perturbing Function in Elliptic Orbital Elements; 8.5 Explicit First-Order Planetary Theory for the Osculating Elements; 8.5.1 Perturbation of the Mean Longitude; 8.6 Small Divisors; 8.7 Long-Term Evolution of Our Planetary System; 9 Resonances; 9.1 Mean Motion Resonances in Our Planetary System; 9.1.1 The 13:8 Resonance between Venus and Earth; 9.1.2 The 1:1 Mean Motion Resonance: Trojan Asteroids; 9.2 Method of Laplace-Lagrange; 9.3 Secular Resonances 9.3.1 Asteroids with Small Inclinations and Eccentricities |
| Record Nr. | UNINA-9910821096803321 |
|
Dvorak R
|
||
| Weinheim, Germany, : Wiley-VCH Verlag GmbH & Co. KGaA, 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||