## The Restless Universe Applications of Gravitational N-Body Dynamics to Planetary Stellar and Galactic SystemsThe Restless Universe: Applications of Gravitational N-Body Dynamics to Planetary Stellar and Galactic Systems stimulates the cross-fertilization of ideas, methods, and applications among the different communities who work in the gravitational N-body problem arena, across diverse fields of astrophysics. The chapters and topics cover three broad themes: the dynamics of the solar system, the dynamics of galaxies and star clusters, and the large scale structure of the universe. The book is essential reading for scientists and graduate students studying N-body dynamics, from the fundamental techniques to the cutting edge of modern research in planetary, stellar, and galactic systems. |

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### Contents

1 | |

On the Trojan problem | 21 |

Ideal resonance and Melnikovs theorem | 43 |

The Yarkovsky effect in the dynamics of the Solar System | 53 |

Are science and celestial mechanics deterministic? Henri Poincare philosopher and scientist | 79 |

Regularisation methods for the Nbody problem | 93 |

Escape in Hills problem | 109 |

from kinematics to dynamics | 129 |

past present and future | 217 |

Gravitational Nbody simulation of largescale cosmic structure | 239 |

Periodic orbits of the planar Nbody problem with equal masses and all bodies on the same path | 265 |

Central configurations revisited | 285 |

Surfaces of separation in the Caledonian symmetrical double binary four body problem | 301 |

The Fast Lyapunov Indicator | 327 |

Determination of chaotic attractors in short discrete time series | 339 |

Nonintegrability in gravitational and cosmological models | 361 |

### Common terms and phrases

Aarseth algorithm approximation asteroid belt asteroids Astron behaviour binary body problem celestial central configuration chaotic choreographies cluster codes coefficients collision collisionless component computed consider constant coordinates corresponding cosmological curves dark matter defined density differential equations disk distance distribution dynamics eccentricity elliptical elliptical galaxies energy equations of motion escape eulerian evolution example expansion Farinella Figure fluid Fourier frequencies function galactic galaxy gravitational grid halo Hamiltonian system initial conditions instability integral iterative libration linear Lyapunov Lyapunov exponents mass matrix method MNRAS N-body simulations observed obtained orbits parameters particles peculiar velocity perturbation phase space physical planetesimal planets Poincare points Poisson equation polynomial potential properties radial real motion redshift surveys region resonance scale Section secular resonances semimajor axis solar system solution stable stars stellar structure surface techniques theorem theory torus transformation Trojan Trojan asteroids variables variational equations vector Vokrouhlicky Yarkovsky effect Ziglin

### Popular passages

Page v - Interactions at High Energy 8 1967 Methods in Solid State and Superfluid Theory 9 1968 Physics of Hot Plasmas 10 1969 Quantum Optics 11 1970 Hadronic Interactions of Photons and Electrons 12 1971 Atoms and Molecules in Astrophysics 13 1972 Properties of Amorphous Semiconductors 14 1973 Phenomenology of Particles at High Energy 15 1974 The Helium Liquids 16 1975 Non-linear Optics 17 1976 Fundamentals of Quark Models 18 1977 Nuclear Structure Physics 19 1978 Metal Non-metal Transitions in Disordered...

Page v - Proceedings (continued) 35 1988 Laser-Plasma Interactions: 4 36 1989 Physics of the Early Universe 37 1990 Pattern Recognition and Image Processing 38 1991 Physics of Nanostructures 39 1991 High Temperature Superconductivity 40 1992 Quantitative Microbeam Analysis 41 1992 Spatial Complexity in Optical Systems 42 1993 High Energy Phenomenology 43 1994 Determination of Geophysical Parameters from Space 44...

Page 337 - C, and Celletti A, 1992. The measure of chaos by the numerical analysis of the fundamental frequencies. Application to the standard mapping, Physica D, 56 253.

Page v - Quantitative Electron Microscopy 26 1983 Statistical and Particle Physics 27 1984 Fundamental Forces 28 1985 Superstrings and Supergravity 29 1985 Laser-Plasma Interactions 3 30 1985 Synchrotron Radiation 31 1986 Localisation and Interaction 32 1987 Computational Physics 33 1987 Astrophysical...