LEADER 05450nam 2200733Ia 450 001 9910821096803321 005 20230803021408.0 010 $a9783527651870 010 $a352765187X 010 $a9783527651856 010 $a3527651853 010 $a9783527651887 010 $a3527651888 035 $a(CKB)2550000001106846 035 $a(EBL)1329759 035 $a(OCoLC)854977485 035 $a(SSID)ssj0001034852 035 $a(PQKBManifestationID)11598979 035 $a(PQKBTitleCode)TC0001034852 035 $a(PQKBWorkID)11016056 035 $a(PQKB)10482450 035 $a(MiAaPQ)EBC1329759 035 $a(Au-PeEL)EBL1329759 035 $a(CaPaEBR)ebr10740141 035 $a(CaONFJC)MIL507216 035 $a(Perlego)1002053 035 $a(EXLCZ)992550000001106846 100 $a20121015d2013 uy 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aCelestial dynamics $echaoticity and dynamics of celestial systems /$fRudolf Dvorak and Christoph Lhotka 205 $a1st ed. 210 $aWeinheim, Germany $cWiley-VCH Verlag GmbH & Co. KGaA$d2013 215 $a1 online resource (323 p.) 300 $aDescription based upon print version of record. 311 08$a9783527409778 311 08$a3527409777 311 08$a9781299759657 311 08$a1299759653 320 $aIncludes bibliographical references (p. 295-304) and index. 327 $aCelestial 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 327 $a3.3.4 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 Froeschle?-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 327 $a5.6 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 327 $a7.2 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 327 $a8.3 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 327 $a9.3.1 Asteroids with Small Inclinations and Eccentricities 330 $aWritten by an internationally renowned expert author and researcher, this monograph fills the need for a book conveying the sophisticated tools needed to calculate exo-planet motion and interplanetary space flight. It is unique in considering the critical problems of dynamics and stability, making use of the software Mathematica, including supplements for practical use of the formulae. A must-have for astronomers and applied mathematicians alike. 606 $aCelestial mechanics 606 $aDifferentiable dynamical systems 615 0$aCelestial mechanics. 615 0$aDifferentiable dynamical systems. 676 $a521 700 $aDvorak$b R$01649401 701 $aLhotka$b Christoph$01649402 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910821096803321 996 $aCelestial dynamics$93998124 997 $aUNINA