6533b871fe1ef96bd12d1c55
RESEARCH PRODUCT
High order normal form construction near the elliptic orbit of the Sitnikov problem
Sara Di RuzzaChristoph Lhotkasubject
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 expansionsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-09-22 |