2013
DOI: 10.1007/s40295-015-0033-5
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Deprit’s Elimination of the Parallax Revisited

Abstract: An extension of Deprit's elimination of the parallax is proposed. This extension takes advantage of the flexibility of the Lie-Deprit method, when the inverse of the Lie operator is applied in order to calculate the generating function of this Lie transform. We have found that, under certain conditions, a function F n , belonging to the null space of the Lie operator, can be added to the generating function of the transform at each order, so that the argument of the perigee, and therefore the argument of latit… Show more

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Cited by 6 publications
(7 citation statements)
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“…Besides, from the viewpoint of a practitioner, the straightforward composition of the sequence formed by the elimination of the parallax and the consequent elimination of the perigee into a single Lie transformation produces a notable increase in the size of the transformation equations, with the consequent deterioration in the evaluation of the periodic terms of the solution, cf. (San-Juan et al 2013). This latter result was in fact expected due to the clear advantages provided by the divide et impera strategy, which is central to Deprit's Hamiltonian simplification concept.…”
mentioning
confidence: 85%
“…Besides, from the viewpoint of a practitioner, the straightforward composition of the sequence formed by the elimination of the parallax and the consequent elimination of the perigee into a single Lie transformation produces a notable increase in the size of the transformation equations, with the consequent deterioration in the evaluation of the periodic terms of the solution, cf. (San-Juan et al 2013). This latter result was in fact expected due to the clear advantages provided by the divide et impera strategy, which is central to Deprit's Hamiltonian simplification concept.…”
mentioning
confidence: 85%
“…represents a small parameter [9,18] which is defined as ν/n, where n is the mean motion of the orbiter. In order to reveal the qualitative behavior of the dynamic system given in (4), we use two Lie transforms: the elimination of the parallax [19][20][21], in order to reduce the number of terms of the transformed Hamiltonian, and the double normalization [22,23], to remove simultaneously the short-and medium-period terms. As a consequence, the system is reduced to an integrable one governed by a truncated second-order closed-form Hamiltonian.…”
Section: Dynamical Modelmentioning
confidence: 99%
“…The procedure for making the argument of the perigee cyclic in the first place follows an analogous strategy to the one devised in the classical elimination of the perigee transformation [2]. However, in our approach it is applied directly to the original main problem Hamiltonian, and differs from the original technique, as well as from an analogous procedure carried out in [56], in which the parallactic terms (inverse powers of the radius with exponents higher than 2) are not removed from the new, partially normalized Hamiltonian. In spite of that, we did not find trouble in dealing with the equation of the center in closed form in the subsequent Delaunay normalization [17], a convenience that might had been anticipated from the discussions in [50].…”
Section: Introductionmentioning
confidence: 99%
“…We extended the complete normalization to the order six of the perturbation approach, which, to our knowledge, is the maximum order that has been reported in the literature (yet limited to partial normalization cases) [25,56]. The aim of computing such a high order is not to enter a competition.…”
Section: Introductionmentioning
confidence: 99%