The reducing transformation and Apocentric Librators

DOI10.1007/BF01238924zbMath0602.70013MaRDI QIDQ3738632

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Publication date: 1986

Published in: Celestial Mechanics (Search for Journal in Brave)

zbMATH Keywords

perturbationcanonical transformationreducing transformationmapping techniqueapocentric libratorsaveraged planar planetary problem near resonancedeep resonance regionfirst order resonant Hamiltonianone degree of freedom problemphase space of the average problemtwo libration mechanism

Mathematics Subject Classification ID

Three-body problems (70F07) Computational methods for problems pertaining to mechanics of particles and systems (70-08) Celestial mechanics (70F15) Nonlinear resonances for nonlinear problems in mechanics (70K30) Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics (70G10)

Related Items (9)

Singularly weighted symplectic forms and applications to asteroid motion ⋮ Review of the dynamics in the Kirkwood gaps ⋮ A simple generalization of Wisdom's perturbative method ⋮ On the dynamics in the asteroids belt. I: General theory ⋮ On resonance ⋮ An integrable model for first-order three-planet mean motion resonances ⋮ Normal forms for the Laplace resonance ⋮ A perturbation method for problems with two critical arguments ⋮ Note on the reducing transformation and secular coupling

Cites Work

• A second fundamental model for resonance
• Motion of two planets with periods commensurable in the ratio 2?1 solutions of the hori auxiliary system
• Canonical solution of the two critical argument problem

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