Long Term Dynamics for the Restricted $N$-Body Problem with Mean Motion Resonances and Crossing Singularities

DOI10.1137/17M1155703zbMath1409.70006arXiv1701.09106MaRDI QIDQ3176282

Stefano Marò, Giovanni Federico Gronchi

Publication date: 19 July 2018

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.09106

zbMATH Keywords

resonancesaveragingrestricted \(N\)-body problemcrossing singularities

Mathematics Subject Classification ID

Celestial mechanics (70F15) Perturbation theories for problems in Hamiltonian and Lagrangian mechanics (70H09) Collisions in celestial mechanics, regularization (70F16)

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Proper elements for resonant planet-crossing asteroids

Cites Work

• The evolution of the orbit distance in the double averaged restricted 3-body problem with crossing singularities
• Dynamics of Earth-crossing asteroids: The protected Toro orbits
• Averaging on Earth-crossing orbits
• Generalized averaging principle and the secular evolution of planet crossing orbits
• On the uncertainty of the minimal distance between two confocal Keplerian orbits
• The analysis of restricted circular twice-averaged three body problem in the case of close orbits
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