Some Rigorous Results on the 1:1 Resonance of the Spin-Orbit Problem

DOI10.1137/19M1294241zbMath1476.70051MaRDI QIDQ4983504

Mauricio Misquero, Rafael Ortega

Publication date: 20 April 2021

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

zbMATH Keywords

asymptotic stabilityforced pendulumdissipative systemssynchronous resonancespin-orbit problemcapture into resonance

Mathematics Subject Classification ID

Problems involving a system of particles with friction (70F40) Celestial mechanics (70F15) Dynamical systems in classical and celestial mechanics (37N05) Parametric resonances for nonlinear problems in mechanics (70K28) Synchronization of solutions to ordinary differential equations (34D06)

Related Items (2)

Uniform bifurcation of comet-type periodic orbits in the restricted \((n + 1)\)-body problem with non-Newtonian homogeneous potential ⋮ The spin-spin problem in celestial mechanics

Cites Work

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• Best constant in Sobolev inequality
• Stable odd solutions of some periodic equations modeling satellite motion.
• Accurate modelling of the low-order secondary resonances in the spin-orbit problem
• A Variational Approach to Lyapunov Type Inequalities
• Solar System Dynamics
• A Lyapunov-type stability criterion using $L^\alpha $ norms
• Chaotic Rotations of a Rigid Ellipsoidal Body Exhibiting Spin-Orbit Misalignment in a Periodic Orbit

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