High order normal form construction near the elliptic orbit of the Sitnikov problem |
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| Authors: | Sara Di Ruzza Christoph Lhotka |
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| Institution: | 1.Dipartimento di Matematica,Università di Roma Tor Vergata,Roma,Italy |
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| Abstract: | 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. |
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