Stability and Chaos in Celestial MechanicsThis overview of classical celestial mechanics focuses the interplay with dynamical systems. Paradigmatic models introduce key concepts – order, chaos, invariant curves and cantori – followed by the investigation of dynamical systems with numerical methods. |
Contents
| 1 | |
2 Numerical dynamical methods | 20 |
3 Keplers problem | 39 |
4 The threebody problem and the Lagrangian solutions | 62 |
5 Rotational dynamics | 83 |
6 Perturbation theory | 107 |
7 Invariant tori | 126 |
8 Longtime stability | 177 |
A Basics of Hamiltonian dynamics | 227 |
B The sphere of influence | 236 |
C Expansion of the perturbing function | 239 |
D Floquet theory and Lyapunov exponents | 240 |
E The planetary problem | 241 |
F Yoshidas symplectic integrator | 245 |
G Astronomical data | 247 |
References | 250 |
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Common terms and phrases
action-angle action-angle variables angle approximation associated assume attractor barycenter Birkhoff normal form canonical transformation Celestial Mechanics Celletti chaotic coefficients computed conjugated constant coordinates corresponding defined denotes diophantine dissipative dynamical system eccentricity eigenvalues elliptic equations of motion equilibrium position exists expand Fourier frequency given Hamilton's equations Hamiltonian function Hamiltonian system initial conditions integrable introduce invariant tori iterations KAM theorem Kepler's Keplerian Lagrangian librational linear Lyapunov exponents mass matrix obtains P₁ periodic orbits perturbation theory perturbing function perturbing parameter phase space planar plane provides r₁ radius reference frame resonance restricted three-body problem rigid body rotation number satellite satisfy Section semimajor axis solution spin-orbit problem stability standard map suitable theorem torus trajectory true anomaly two-body problem unperturbed Hamiltonian values vector velocity zero მყ