1:1 Ground track resonance in a uniformly rotating 4th degree and order gravitational field

Jinglang Feng, Ron Noomen, Xiyun Hou, Pieter Visser, Jianping Yuan

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Using a gravitational field truncated at the 4th degree and order, the 1:1 ground-track resonance is studied. To address the main properties of this resonance, a 1-degree of freedom (1-DOF) system is firstly studied. Equilibrium points (EPs), stability and resonance width are obtained. Different from previous studies, the inclusion of non-spherical terms higher than degree and order 2 introduces new phenomena. For a further study about this resonance, a 2-DOF model which includes a main resonance term (the 1-DOF system) and a perturbing resonance term is studied. With the aid of Poincaré sections, the generation of chaos in the phase space is studied in detail by addressing the overlap process of these two resonances with arbitrary combinations of eccentricity (e) and inclination (i). Retrograde orbits, near circular orbits and near polar orbits are found to have better stability against the perturbation of the second resonance. The situations of complete chaos are estimated in the e−i plane. By applying the maximum Lyapunov Characteristic Exponent (LCE), chaos is characterized quantitatively and similar conclusions can be achieved. This study is applied to three asteroids 1996 HW1, Vesta and Betulia, but the conclusions are not restricted to them.
LanguageEnglish
Pages67-93
Number of pages27
JournalCelestial Mechanics and Dynamical Astronomy
Volume127
Issue number1
Early online date12 Sep 2016
DOIs
Publication statusPublished - 31 Jan 2017

Fingerprint

ground tracks
Gravitational Field
gravitational fields
Rotating
chaotic dynamics
Chaos theory
chaos
Chaos
Orbits
Orbit
Term
degrees of freedom
Degree of freedom
retrograde orbits
polar orbits
Poincaré Section
Asteroids
Characteristic Exponents
Eccentricity
circular orbits

Keywords

  • asteroid
  • resonance width
  • stability
  • chaos
  • Poincaré sections
  • equilibrium points (EPs)

Cite this

Feng, Jinglang ; Noomen, Ron ; Hou, Xiyun ; Visser, Pieter ; Yuan, Jianping. / 1:1 Ground track resonance in a uniformly rotating 4th degree and order gravitational field. In: Celestial Mechanics and Dynamical Astronomy. 2017 ; Vol. 127, No. 1. pp. 67-93.
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1:1 Ground track resonance in a uniformly rotating 4th degree and order gravitational field. / Feng, Jinglang; Noomen, Ron; Hou, Xiyun; Visser, Pieter; Yuan, Jianping.

In: Celestial Mechanics and Dynamical Astronomy, Vol. 127, No. 1, 31.01.2017, p. 67-93.

Research output: Contribution to journalArticle

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AB - Using a gravitational field truncated at the 4th degree and order, the 1:1 ground-track resonance is studied. To address the main properties of this resonance, a 1-degree of freedom (1-DOF) system is firstly studied. Equilibrium points (EPs), stability and resonance width are obtained. Different from previous studies, the inclusion of non-spherical terms higher than degree and order 2 introduces new phenomena. For a further study about this resonance, a 2-DOF model which includes a main resonance term (the 1-DOF system) and a perturbing resonance term is studied. With the aid of Poincaré sections, the generation of chaos in the phase space is studied in detail by addressing the overlap process of these two resonances with arbitrary combinations of eccentricity (e) and inclination (i). Retrograde orbits, near circular orbits and near polar orbits are found to have better stability against the perturbation of the second resonance. The situations of complete chaos are estimated in the e−i plane. By applying the maximum Lyapunov Characteristic Exponent (LCE), chaos is characterized quantitatively and similar conclusions can be achieved. This study is applied to three asteroids 1996 HW1, Vesta and Betulia, but the conclusions are not restricted to them.

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