Boundary curves for families of planar orbits

Bozis, George; Ichtiaroglou, S.

doi:10.1007/bf00692011

Cited by 27 publications

(21 citation statements)

References 5 publications

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“…, введено понятие семейства граничных кривых (СГК) [7]. При этом все члены семейства орбит расположены в допустимой области плоскости xy, определяемой соответствующим СГК с общей энергией ( )…”

Section: обсуждение альтернативные подходы к решению обратной задачиunclassified

To the Inverse Problem of Celestial Mechanics

Omarova¹,

Omarova²

2021

SPM

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Section: обсуждение альтернативные подходы к решению обратной задачиunclassified

To the Inverse Problem of Celestial Mechanics

Omarova¹,

Omarova²

2021

SPM

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“…defines the region on the (x, y) plane (Bozis & Ichtiaroglou, 1994), where motion is allowed for the members of the family (3). If we insert expressions ( 2) and (3) in equation ( 4) and demand that all coefficients of equal powers in x and y be zero we find…”

Section: The Potential Associated With the Family Of Accurate Periodi...mentioning

confidence: 99%

Using new dynamical indicators to distinguish between order and chaos in a galactic potential producing exact periodic orbits and chaotic components

Zotos

2013

Preprint

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The theory of the inverse problem is used in order to find a two dimensional galactic potential generating a mono-parametric family of elliptic periodic orbits. The potential is made up of a two-dimensional harmonic oscillator with perturbing terms of third and fourth degree and can be considered to describe local motion in the central parts of a barred galaxy. Our numerical calculations indicate that the potential produces also other families of orbits and there are cases, where distinct chaotic components are also observed. The numerical experiments suggest that there are regular as well as chaotic orbits supporting the barred structure. We use a variety of dynamical indicators, in order to determine the character of motion. Of significant interest, is the S(g) dynamical spectrum, which is used in order to identify the islandic motion of resonant orbits and also proves to be a very useful and fast indicator, in order to distinguish between regular and chaotic motion. Comparison with other methods for detecting chaos is also discussed. The present results are compared with outcomes from earlier work.

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“…Those are curves defining regions B(x, y) ≥ 0 where motion of the particle may take place (as the particle moves on various members of the same family), with total energy generally varying from member to member (Bozis & Ichtiaroglou 1994). We know that to each pair (V, γ) of a potential and a family there corresponds a specific FBC.…”

Section: Introductionmentioning

confidence: 99%

“…Szebehely's equation was aimed to be used for the determination of the potential of the Earth by means of satellite observations. The form of Szebehely's equation allowed Bozis & Ichtiaroglou (1994) to state that the orbits of the family are actually traced only in a region which is limited by the family boundary curves (FBC). Later on, Bozis (1996) and Anisiu & Bozis (2000) considered the following related problem: given a planar region, find the potential and the families of curves described by a particle precisely in the given region (programmed to remain trapped into it).…”

Section: Introductionmentioning

confidence: 99%

Programmed motion in the presence of homogeneity

Bozis

Anisiu

2009

Astron Nachr

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In the framework of the inverse problem of dynamics, we face the following question with reference to the motion of one material point: Given a region T orb of the xy plane, described by the inequality g(x, y) ≤ c0, are there potentials V = V (x, y) which can produce monoparametric families of orbits f (x, y) = c (also to be found) lying exclusively in the region T orb ? As the relevant PDEs are nonlinear, an answer to this question (generally affirmative, but not with assurance) can be given by the procedure of the determination of certain constants specifying the pertinent functions. In this paper we ease the mathematics involved by making certain simplifying assumptions referring to the homogeneity of both the function g(x, y) (describing the boundary of T orb ) and of the slope function γ(x, y) = fy/fx (representing the required family f (x, y) = c). We develop the method to treat the so formulated problem and we show that, even under these restrictive assumptions, an affirmative answer is guaranteed provided that two algebraic equations have in common at least one solution.

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Boundary curves for families of planar orbits

Cited by 27 publications

References 5 publications

To the Inverse Problem of Celestial Mechanics

To the Inverse Problem of Celestial Mechanics

Using new dynamical indicators to distinguish between order and chaos in a galactic potential producing exact periodic orbits and chaotic components

Programmed motion in the presence of homogeneity

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