Accurate modelling of the low-order secondary resonances in the spin-orbit problem
| Autor: | Alessandra Celletti, Giuseppe Pucacco, Christos Efthymiopoulos, Ioannis Gkolias |
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| Rok vydání: | 2019 |
| Předmět: |
Normal form
FOS: Physical sciences Dynamical Systems (math.DS) 01 natural sciences Primary and secondary resonances Spin-orbit problem 010305 fluids & plasmas 0103 physical sciences FOS: Mathematics Mathematics - Dynamical Systems 010306 general physics Settore MAT/07 - Fisica Matematica Mathematical Physics Bifurcation Spin-½ Earth and Planetary Astrophysics (astro-ph.EP) Physics Numerical Analysis Series (mathematics) Phase portrait Applied Mathematics Mathematical analysis Time evolution Resonance Mathematical Physics (math-ph) Modeling and Simulation Phase space Orbit (dynamics) Astrophysics - Earth and Planetary Astrophysics |
| Zdroj: | Communications in Nonlinear Science and Numerical Simulation. 77:181-202 |
| ISSN: | 1007-5704 |
| Popis: | We provide an analytical approximation to the dynamics in each of the three most important low order secondary resonances (1:1, 2:1, and 3:1) bifurcating from the synchronous primary resonance in the gravitational spin-orbit problem. To this end we extend the perturbative approach introduced in Gkolias et. al. (2016), based on normal form series computations. This allows to recover analytically all non-trivial features of the phase space topology and bifurcations associated with these resonances. Applications include the characterization of spin states of irregular planetary satellites or double systems of minor bodies with irregular shapes. The key ingredients of our method are: i) the use of a detuning parameter measuring the distance from the exact resonance, and ii) an efficient scheme to `book-keep' the series terms, which allows to simultaneously treat all small parameters entering the problem. Explicit formulas are provided for each secondary resonance, yielding i) the time evolution of the spin state, ii) the form of phase portraits, iii) initial conditions and stability for periodic solutions, and iv) bifurcation diagrams associated with the periodic orbits. We give also error estimates of the method, based on analyzing the asymptotic behavior of the remainder of the normal form series. Comment: Accepted for publication in Communications in Nonlinear Science and Numerical Simulation |
| Databáze: | OpenAIRE |
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