Integrability of close encounters in the spatial restricted three-body problem

DOI10.1142/S0219199721500401zbMath1505.70031arXiv1809.01257MaRDI QIDQ5095851

Franco Cardin, Massimilliano Guzzo

Publication date: 11 August 2022

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.01257

zbMATH Keywords

Hamilton-Jacobi equationcomplete integrabilitycollisionKustaanheimo-Stiefel regularizationseries solition

Mathematics Subject Classification ID

Three-body problems (70F07) Hamilton-Jacobi equations in mechanics (70H20) Collisions in celestial mechanics, regularization (70F16)

Related Items (1)

Theory and applications of fast Lyapunov indicators to model problems of celestial mechanics

Cites Work

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• The planetary \(N\)-body problem: symplectic foliation, reductions and invariant tori
• Canonical elements for Öpik theory
• Quaternions and the perturbed Kepler problem
• The Kustaanheimo-Stiefel map, the Hopf fibration and the square root map on \(\mathbb R^{3}\) and \(\mathbb R^{4}\)
• Geometric chaos indicators and computations of the spherical hypertube manifolds of the spatial circular restricted three-body problem
• Dynamics in the center manifold of the collinear points of the restricted three-body problem
• Quasiperiodic motions in the planar three-body problem
• Lissajous and halo orbits in the restricted three-body problem
• Regular and singular reductions in the spatial three-body problem
• Asymptotic density of collision orbits in the restricted circular planar 3 body problem
• Integrability of the spatial restricted three-body problem near collisions (an announcement)
• Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
• Kustaanheimo-Stiefel regularization and the quadrupolar conjugacy
• Consecutive quasi-collisions in the planar circular RTBP
• Quasi‐Periodic Almost‐Collision Orbits in the Spatial Three‐Body Problem
• A note on the existence of invariant punctured tori in the planar circular restricted three-body problem
• The Levi-Civita, KS and Radial-Inversion Regularizing Transformations
• Connecting orbits and invariant manifolds in the spatial restricted three-body problem
• Global Aspects of Classical Integrable Systems
• Démonstration du ‘théorème d'Arnold’ sur la stabilité du système planétaire (d'après Herman)
• SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS
• Perturbation theory of Kepler motion based on spinor regularization.
• Regularization of kepler's problem and the averaging method on a manifold
• Low Energy Transit Orbits in the Restricted Three-Body Problems
• Averaging the planar three-body problem in the neighborhood of double inner collisions

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