0000000000780431

AUTHOR

Christoph Lhotka

showing 2 related works from this author

Nearly-integrable dissipative systems and celestial mechanics

2010

The influence of dissipative effects on classical dynamical models of Celestial Mechanics is of basic importance. We introduce the reader to the subject, giving classical examples found in the literature, like the standard map, the Hénon map, the logistic mapping. In the framework of the dissipative standard map, we investigate the existence of periodic orbits as a function of the parameters. We also provide some techniques to compute the breakdown threshold of quasi-periodic attractors. Next, we review a simple model of Celestial Mechanics, known as the spin-orbit problem which is closely linked to the dissipative standard map. In this context we present the conservative and dissipative KA…

PhysicsDynamical systems theoryKolmogorov–Arnold–Moser theoremGeneral Physics and AstronomyStandard mapInvariant (physics)Three-body problemCelestial mechanicsPhysics and Astronomy (all)Classical mechanicsAttractorIntegrable systemsDissipative systemGeneral Materials ScienceMaterials Science (all)Physical and Theoretical ChemistryMaterials Science (all); Physics and Astronomy (all); Physical and Theoretical ChemistrySettore MAT/07 - Fisica MatematicaThe European Physical Journal Special Topics
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High order normal form construction near the elliptic orbit of the Sitnikov problem

2011

We consider the Sitnikov problem; from the equations of motion we derive the approximate Hamiltonian flow. Then, we introduce suitable action–angle variables in order to construct a high order normal form of the Hamiltonian. We introduce Birkhoff Cartesian coordinates near the elliptic orbit and we analyze the behavior of the remainder of the normal form. Finally, we derive a kind of local stability estimate in the vicinity of the periodic orbit for exponentially long times using the normal form up to 40th order in Cartesian coordinates.

Elliptic orbitNormal formPerturbation theoryExponential stabilitylaw.inventionsymbols.namesakeExponential stabilitylawCartesian coordinate systemHigh orderRemainderSettore MAT/07 - Fisica MatematicaMathematical PhysicsMathematicsApplied MathematicsMathematical analysisBirkhoff coordinatesEquations of motionAstronomy and AstrophysicsSitnikov problemComputational MathematicsSpace and Planetary ScienceModeling and SimulationSitnikov problemsymbolsBirkhoff coordinates; Exponential stability; Lie-series expansions; Normal form; Perturbation theory; Sitnikov problem; Astronomy and Astrophysics; Space and Planetary ScienceHamiltonian (quantum mechanics)Lie-series expansions
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