NDLI: Intermediary orbits for oscillating motions

Content Provider	Springer Nature Link
Author	Oberti, P. Pocart, B.
Copyright Year	2011
Abstract	Hamiltonian approximations generally result from series expansions and truncations at different orders. But other ways are possible, and some of them, as the one this paper tries to explore, can speed up Hamiltonian computations and prove useful for studies involving extensive developments, for example solar system bodies with complex dynamics or requiring accurate ephemeris for observational purposes.Reflecting a property of the frequency of motion of the pendulum’s Hamiltonian, a fast convergent algorithm aimed to build pendulum approximations was outlined in a completely different way that the classical development in powers of the libration angle. With convenient initial conditions, the first two steps of the algorithm lead to approximate Hamiltonians explicitly expressed in the normalizing action variable and offering solutions easily obtained through Kepler-like equations, hence providing useful intermediary orbits for the Lie transformation algorithm.Numerical checks showed a good efficiency and consistency of these solutions up to rather large libration amplitudes: for libration angles up to 300 degrees, only half the steps required by the classical development algorithm sufficed for this one to mimic the pendulum, and the second step’s solution outrun its classical counterpart up to 90 degrees.
Starting Page	71
Ending Page	78
Page Count	8
File Format	PDF
ISSN	0004640X
Journal	Astrophysics and Space Science
Volume Number	333
Issue Number	1
e-ISSN	1572946X
Language	English
Publisher	Springer Netherlands
Publisher Date	2011-02-03
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Hamiltonian systems Integrability Resonance Celestial mechanics Solar system bodies Astronomy, Observations and Techniques
Content Type	Text
Resource Type	Article
Subject	Astronomy and Astrophysics Space and Planetary Science

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