TY - JOUR
T1 - 1:1 Ground-track resonance in a uniformly rotating 4th degree and order gravitational field
AU - Feng, Jinglang
AU - Noomen, Ron
AU - Hou, Xiyun
AU - Visser, Pieter
AU - Yuan, Jianping
PY - 2017/1/1
Y1 - 2017/1/1
N2 - 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.
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.
KW - 1996 HW1
KW - Asteroid
KW - Betulia
KW - Chaos
KW - Equilibrium Points (EPs)
KW - Poincaré sections
KW - Resonance width
KW - Stability
KW - Vesta
UR - http://resolver.tudelft.nl/uuid:a7ffb975-b4f2-498b-9864-a7b076fabda8
UR - http://www.scopus.com/inward/record.url?scp=84987648007&partnerID=8YFLogxK
U2 - 10.1007/s10569-016-9717-9
DO - 10.1007/s10569-016-9717-9
M3 - Article
AN - SCOPUS:84987648007
SN - 0923-2958
VL - 127
SP - 67
EP - 93
JO - Celestial Mechanics and Dynamical Astronomy: an international journal of space dynamics
JF - Celestial Mechanics and Dynamical Astronomy: an international journal of space dynamics
IS - 1
ER -