Search results for "Sitnikov problem"

showing 2 items of 2 documents

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
researchProduct

Invariant rotational curves in Sitnikov's Problem

1993

The Sitnikov's Problem is a Restricted Three-Body Problem of Celestial Mechanics depending on a parameter, the eccentricity,e. The Hamiltonian,H(z, v, t, e), does not depend ont ife=0 and we have an integrable system; ife is small the KAM Theory proves the existence of invariant rotational curves, IRC. For larger eccentricities, we show that there exist two complementary sequences of intervals of values ofe that accumulate to the maximum admissible value of the eccentricity, 1, and such that, for one of the sequences IRC around a fixed point persist. Moreover, they shrink to the planez=0 ase tends to 1.

Kolmogorov–Arnold–Moser theoremApplied MathematicsMathematical analysisKepler's laws of planetary motionAstronomy and AstrophysicsGeometryInvariant (physics)Fixed pointThree-body problemSitnikov problemCelestial mechanicsComputational Mathematicssymbols.namesakeSpace and Planetary ScienceModeling and SimulationsymbolsAstrophysics::Earth and Planetary AstrophysicsHamiltonian (quantum mechanics)Mathematical PhysicsMathematicsCelestial Mechanics & Dynamical Astronomy
researchProduct