Control of chaos in the vicinity of the Earth-Moon L5 Lagrangian point to keep a spacecraft in orbit

J. Slíz, A. Süli, T. Kovács

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The concept of Space Manifold Dynamics is a new method of space research. We have applied it along with the basic idea of the method of Ott, Grebogi, and York (OGY method) to stabilize the motion of a spacecraft around the triangular Lagrange point L5 of the Earth-Moon system. We have determined the escape rate of the trajectories in the general three- and four-body problem and estimated the average lifetime of the particles. Integrating the two models we mapped in detail the phase space around the L5 point of the Earth-Moon system. Using the phase space portrait our next goal was to apply a modified OGY method to keep a spacecraft close to the vicinity of L5. We modified the equation of motions with the addition of a time dependent force to the motion of the spacecraft. In our orbit-keeping procedure there are three free parameters: (i) the magnitude of the thrust, (ii) the start time, and (iii) the length of the control. Based on our numerical experiments we were able to determine possible values for these parameters and successfully apply a control phase to a spacecraft to keep it on orbit around L5. (

Original languageEnglish
Pages (from-to)23-31
Number of pages9
JournalAstronomische Nachrichten
Volume336
Issue number1
DOIs
Publication statusPublished - Feb 1 2015

Fingerprint

chaotic dynamics
moon
Moon
chaos
spacecraft
Earth-Moon system
orbits
four body problem
phase control
thrust
escape
equations of motion
trajectory
trajectories
life (durability)
method
experiment
parameter

Keywords

  • Chaos
  • Earth
  • Methods: N-body simulations
  • Methods: numerical
  • Moon

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

Control of chaos in the vicinity of the Earth-Moon L5 Lagrangian point to keep a spacecraft in orbit. / Slíz, J.; Süli, A.; Kovács, T.

In: Astronomische Nachrichten, Vol. 336, No. 1, 01.02.2015, p. 23-31.

Research output: Contribution to journalArticle

@article{453121025275432cb2ece8ae28cdcdac,
title = "Control of chaos in the vicinity of the Earth-Moon L5 Lagrangian point to keep a spacecraft in orbit",
abstract = "The concept of Space Manifold Dynamics is a new method of space research. We have applied it along with the basic idea of the method of Ott, Grebogi, and York (OGY method) to stabilize the motion of a spacecraft around the triangular Lagrange point L5 of the Earth-Moon system. We have determined the escape rate of the trajectories in the general three- and four-body problem and estimated the average lifetime of the particles. Integrating the two models we mapped in detail the phase space around the L5 point of the Earth-Moon system. Using the phase space portrait our next goal was to apply a modified OGY method to keep a spacecraft close to the vicinity of L5. We modified the equation of motions with the addition of a time dependent force to the motion of the spacecraft. In our orbit-keeping procedure there are three free parameters: (i) the magnitude of the thrust, (ii) the start time, and (iii) the length of the control. Based on our numerical experiments we were able to determine possible values for these parameters and successfully apply a control phase to a spacecraft to keep it on orbit around L5. (",
keywords = "Chaos, Earth, Methods: N-body simulations, Methods: numerical, Moon",
author = "J. Sl{\'i}z and A. S{\"u}li and T. Kov{\'a}cs",
year = "2015",
month = "2",
day = "1",
doi = "10.1002/asna.201412132",
language = "English",
volume = "336",
pages = "23--31",
journal = "Astronomische Nachrichten",
issn = "0004-6337",
publisher = "Wiley-VCH Verlag",
number = "1",

}

TY - JOUR

T1 - Control of chaos in the vicinity of the Earth-Moon L5 Lagrangian point to keep a spacecraft in orbit

AU - Slíz, J.

AU - Süli, A.

AU - Kovács, T.

PY - 2015/2/1

Y1 - 2015/2/1

N2 - The concept of Space Manifold Dynamics is a new method of space research. We have applied it along with the basic idea of the method of Ott, Grebogi, and York (OGY method) to stabilize the motion of a spacecraft around the triangular Lagrange point L5 of the Earth-Moon system. We have determined the escape rate of the trajectories in the general three- and four-body problem and estimated the average lifetime of the particles. Integrating the two models we mapped in detail the phase space around the L5 point of the Earth-Moon system. Using the phase space portrait our next goal was to apply a modified OGY method to keep a spacecraft close to the vicinity of L5. We modified the equation of motions with the addition of a time dependent force to the motion of the spacecraft. In our orbit-keeping procedure there are three free parameters: (i) the magnitude of the thrust, (ii) the start time, and (iii) the length of the control. Based on our numerical experiments we were able to determine possible values for these parameters and successfully apply a control phase to a spacecraft to keep it on orbit around L5. (

AB - The concept of Space Manifold Dynamics is a new method of space research. We have applied it along with the basic idea of the method of Ott, Grebogi, and York (OGY method) to stabilize the motion of a spacecraft around the triangular Lagrange point L5 of the Earth-Moon system. We have determined the escape rate of the trajectories in the general three- and four-body problem and estimated the average lifetime of the particles. Integrating the two models we mapped in detail the phase space around the L5 point of the Earth-Moon system. Using the phase space portrait our next goal was to apply a modified OGY method to keep a spacecraft close to the vicinity of L5. We modified the equation of motions with the addition of a time dependent force to the motion of the spacecraft. In our orbit-keeping procedure there are three free parameters: (i) the magnitude of the thrust, (ii) the start time, and (iii) the length of the control. Based on our numerical experiments we were able to determine possible values for these parameters and successfully apply a control phase to a spacecraft to keep it on orbit around L5. (

KW - Chaos

KW - Earth

KW - Methods: N-body simulations

KW - Methods: numerical

KW - Moon

UR - http://www.scopus.com/inward/record.url?scp=84922639874&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84922639874&partnerID=8YFLogxK

U2 - 10.1002/asna.201412132

DO - 10.1002/asna.201412132

M3 - Article

AN - SCOPUS:84922639874

VL - 336

SP - 23

EP - 31

JO - Astronomische Nachrichten

JF - Astronomische Nachrichten

SN - 0004-6337

IS - 1

ER -