Cargando…
Celestial Dynamics : Chaoticity and Dynamics of Celestial Systems.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken :
Wiley,
2013.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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 Index3.3.5 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 Elements5.7 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-Axes7.3 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 Problem8.3.1 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.