caa a22 4500 445863218 CHVBK 20180317145450.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s10569-011-9380-0 doi (NATIONALLICENCE)springer-10.1007/s10569-011-9380-0 High order normal form construction near the elliptic orbit of the Sitnikov problem [Elektronische Daten] [Sara Di Ruzza, Christoph Lhotka] 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. Springer Science+Business Media B.V., 2011 Sitnikov problem nationallicence Normal form nationallicence Birkhoff coordinates nationallicence Exponential stability nationallicence Perturbation theory nationallicence Lie-series expansions nationallicence Di Ruzza Sara Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133, Roma, Italy aut Lhotka Christoph Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133, Roma, Italy aut Celestial Mechanics and Dynamical Astronomy Springer Netherlands 111/4(2011-12-01), 449-464 0923-2958 111:4<449 2011 111 10569 https://doi.org/10.1007/s10569-011-9380-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10569-011-9380-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Di Ruzza Sara Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133, Roma, Italy aut NATIONALLICENCE 700 1- Lhotka Christoph Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133, Roma, Italy aut NATIONALLICENCE 773 0- Celestial Mechanics and Dynamical Astronomy Springer Netherlands 111/4(2011-12-01), 449-464 0923-2958 111:4<449 2011 111 10569 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer