Corpus ID: 235458028

Efficient and accurate KAM tori construction for the dissipative spin-orbit problem using a map reduction

@article{Calleja2021EfficientAA,
  title={Efficient and accurate KAM tori construction for the dissipative spin-orbit problem using a map reduction},
  author={R. Calleja and A. Celletti and J. Gimeno and R. Llave},
  journal={ArXiv},
  year={2021},
  volume={abs/2106.09175}
}
We consider the dissipative spin-orbit problem in Celestial Mechanics, which describes the rotational motion of a triaxial satellite moving on a Keplerian orbit subject to tidal forcing and drift. Our goal is to construct quasi-periodic solutions with fixed frequency, satisfying appropriate conditions. With the goal of applying rigorous KAM theory, we compute such quasi-periodic solution with very high precision. To this end, we have developed a very efficient algorithm. The first step is to… Expand
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References

SHOWING 1-10 OF 91 REFERENCES
Quasi-periodic motions in a special class of dynamical equations with dissipative effects: a pair of detection methods
We consider a particular class of equations of motion, generalizing to n degrees of freedom the "dissipative spin--orbit problem", commonly studied in Celestial Mechanics. Those equations areExpand
Transient times, resonances and drifts of attractors in dissipative rotational dynamics
TLDR
A method is devised which provides a reliable indication on the transient time which is needed to reach an attractor in the spin–orbit model and is based on an analytical result, precisely a suitable normal form construction. Expand
KAM estimates for the dissipative standard map
From the beginning of KAM theory, it was realized that its applicability to realistic problems depended on developing quantitative estimates on the sizes of the perturbations allowed. In this paperExpand
Analysis of resonances in the spin-orbit problem in Celestial Mechanics: The synchronous resonance (Part I)
We study the stability of spin-orbit resonances in Celestial Mechanics, namely the exact commensurabilities between the periods of rotation and revolution of satellites or planets. We introduce aExpand
On the Computation of Reducible Invariant Tori on a Parallel Computer
TLDR
The algorithm presents a high degree of parallelism, and the computational effort grows linearly with the number of Fourier modes needed to represent the solution, for these reasons it is a very good option to compute quasi-periodic solutions with several basic frequencies. Expand
Lissajous and Halo Orbits in the Restricted Three-Body Problem
TLDR
The analytical values obtained after a second order resonant perturbation theory are in very good agreement (in some cases up to the fourth decimal digit) with the numerical values found in the literature. Expand
A parameterization method for the computation of invariant tori andtheir whiskers in quasi-periodic maps: Numerical algorithms
In this paper we develop several numerical algorithms for the computation of invariant manifolds in quasi-periodically forced systems. The invariant manifolds we consider are invariant tori and Expand
A KAM theory for conformally symplectic systems: Efficient algorithms and their validation
Abstract We present a KAM theory for some dissipative systems (geometrically, these are conformally symplectic systems, i.e. systems that transform a symplectic form into a multiple of itself). ForExpand
Computation of invariant tori by Newton-Krylov methods in large-scale dissipative systems
Abstract A method to compute invariant tori in high-dimensional systems, obtained as discretizations of PDEs, by continuation and Newton–Krylov methods is described. Invariant tori are found as fixedExpand
Stability and chaos in celestial mechanics
This book presents classical celestial mechanics and its interplay with dynamical systems in a way suitable for advance level undergraduate students as well as postgraduate students and researchers.Expand
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