## 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

Nbody simulations of the Solar System planet formation and galaxy clusters | 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 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.