### Abstract

A method for directly establishing a linearized dynamics model of relative motion for a satellite formation flying on an arbitrary elliptical reference orbit is presented. The proposed linearized dynamics model of relative motion is intuitive and favorable to be utilized for designing formation control system, implementing guidance algorithm, and analyzing optimization problems etc. An analytical solution for the radius of a reference orbit affected by the J _{2} geopotential disturbance is used to approximate the actual reference orbit rather than directly use the unperturbed standard orbit. The accuracy of the analytical solution directly affects the accuracy of the linear relative motion model of a satellite formation. Thus, emphasis is placed on deducing an accurate analytical solution for a perturbed reference orbit radius, which is analyzed by adding perturbed motion in the radial direction to the corresponding unperturbed reference orbit radius. Furthermore, by considering time-varying angular velocity of an elliptical reference orbit, the analytical solution of a perturbed orbit radius is obtained in the true anomaly domain. In order to better match the actual force conditions of a satellite formation, a perturbed true anomaly and perturbed argument of perigee are adopted and substituted into the gradient of the J_{2} disturbance force. Simulation results indicate the analytical solution for the radius of a perturbed elliptical reference orbit is accurate, and the proposed linear dynamics model of relative motion can track the high-fidelity simulated relative motion more accurately than previously proposed dynamics models, even for an elliptical reference orbit with high eccentricity.

Original language | English |
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Pages (from-to) | 55-69 |

Number of pages | 15 |

Journal | International Journal of Non-Linear Mechanics |

Volume | 55 |

DOIs | |

Publication status | Published - 2013 Jun 3 |

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### All Science Journal Classification (ASJC) codes

- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics

### Cite this

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**Linearized dynamics model for relative motion under a J _{2}- perturbed elliptical reference orbit.** / Wei, Changzhu; Park, Sang Young; Park, Chandeok.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Linearized dynamics model for relative motion under a J2- perturbed elliptical reference orbit

AU - Wei, Changzhu

AU - Park, Sang Young

AU - Park, Chandeok

PY - 2013/6/3

Y1 - 2013/6/3

N2 - A method for directly establishing a linearized dynamics model of relative motion for a satellite formation flying on an arbitrary elliptical reference orbit is presented. The proposed linearized dynamics model of relative motion is intuitive and favorable to be utilized for designing formation control system, implementing guidance algorithm, and analyzing optimization problems etc. An analytical solution for the radius of a reference orbit affected by the J 2 geopotential disturbance is used to approximate the actual reference orbit rather than directly use the unperturbed standard orbit. The accuracy of the analytical solution directly affects the accuracy of the linear relative motion model of a satellite formation. Thus, emphasis is placed on deducing an accurate analytical solution for a perturbed reference orbit radius, which is analyzed by adding perturbed motion in the radial direction to the corresponding unperturbed reference orbit radius. Furthermore, by considering time-varying angular velocity of an elliptical reference orbit, the analytical solution of a perturbed orbit radius is obtained in the true anomaly domain. In order to better match the actual force conditions of a satellite formation, a perturbed true anomaly and perturbed argument of perigee are adopted and substituted into the gradient of the J2 disturbance force. Simulation results indicate the analytical solution for the radius of a perturbed elliptical reference orbit is accurate, and the proposed linear dynamics model of relative motion can track the high-fidelity simulated relative motion more accurately than previously proposed dynamics models, even for an elliptical reference orbit with high eccentricity.

AB - A method for directly establishing a linearized dynamics model of relative motion for a satellite formation flying on an arbitrary elliptical reference orbit is presented. The proposed linearized dynamics model of relative motion is intuitive and favorable to be utilized for designing formation control system, implementing guidance algorithm, and analyzing optimization problems etc. An analytical solution for the radius of a reference orbit affected by the J 2 geopotential disturbance is used to approximate the actual reference orbit rather than directly use the unperturbed standard orbit. The accuracy of the analytical solution directly affects the accuracy of the linear relative motion model of a satellite formation. Thus, emphasis is placed on deducing an accurate analytical solution for a perturbed reference orbit radius, which is analyzed by adding perturbed motion in the radial direction to the corresponding unperturbed reference orbit radius. Furthermore, by considering time-varying angular velocity of an elliptical reference orbit, the analytical solution of a perturbed orbit radius is obtained in the true anomaly domain. In order to better match the actual force conditions of a satellite formation, a perturbed true anomaly and perturbed argument of perigee are adopted and substituted into the gradient of the J2 disturbance force. Simulation results indicate the analytical solution for the radius of a perturbed elliptical reference orbit is accurate, and the proposed linear dynamics model of relative motion can track the high-fidelity simulated relative motion more accurately than previously proposed dynamics models, even for an elliptical reference orbit with high eccentricity.

UR - http://www.scopus.com/inward/record.url?scp=84878329844&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84878329844&partnerID=8YFLogxK

U2 - 10.1016/j.ijnonlinmec.2013.04.016

DO - 10.1016/j.ijnonlinmec.2013.04.016

M3 - Article

AN - SCOPUS:84878329844

VL - 55

SP - 55

EP - 69

JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

SN - 0020-7462

ER -