A satellite relative motion model including $$J_2$$ and $$J_3$$ via Vinti’s intermediary

Biria, Ashley D.; Russell, Ryan P.

doi:10.1007/s10569-017-9806-4

Cited by 16 publications

(10 citation statements)

References 44 publications

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“…However, the concepts of accounting for the second-order nonlinear terms and the abrupt state jumps on relative state uncertainty propagation can be used to extend the current method through combing it with the state-of-art analytical STTs in relative motion (e.g., [8,9,12]).…”

Section: F Summary and Discussionmentioning

confidence: 99%

“…Substituting Eqs. 11, (12) and 14into Eq. 9, a nonlinear propagation from the mean relative orbital elements to the osculating orbital elements under J2-perturbation can be obtained as, i.e.…”

Section: Stts For Relative State In J2-perturbed Elliptic Orbitsmentioning

confidence: 99%

“…Moreover, D'Amico et al [9] formulated the relative motion of two spacecraft in arbitrarily eccentric orbits perturbed by J2 and differential drag by using three different definitions of ROE, Schaub [10,11] proposed a general method to the modelling and control of relative orbit geometry through ROE, and Biria and Russell [12] derived an analytical relative-motion equations including J2 and J3 via Vinti's Intermediary. Although the effects of orbital eccentricity and perturbation had been well-cooperated in these research efforts [4][5][6][7][8][9][10][11][12], they were just linear approximations to the naturally-nonlinear orbital dynamics, which would be insufficient for problems with large separation distance between satellites. To overcome this shortcoming, additional works had been done to account for the effects of nonlinear terms.…”

Section: Introductionmentioning

confidence: 99%

“…the Earth oblateness and atmospheric drag). In fact, based on the LinCov technique [20], all the state transition matrices (STMs) employed in the linear relative-motion models [2][3][4][5][6][7][8][9][10][11][12] can be directly used to propagate the relative state uncertainty. However, as will be revealed in this study, the higher-order nonlinear solution for propagating relative state (e.g., [14]) cannot be directly used for propagate the relative state uncertainty.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Analytical Uncertainty Propagation for Relative Motion near J2-Perturbed Elliptic Orbits

Yang

Luo

Lappas

et al. 2018

Journal of Guidance, Control, and Dynamics

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An analytical uncertainty propagation method based on state transition tensors (STTs) has been developed for satellite relative motion near J2-perturbed, elliptic orbits. The STTs used to propagate the relative state uncertainty are derived by adding a correction into the original STTs for propagating relative state. A new set of transitive STTs is further derived in order to propagate uncertainties for relative motion with abrupt state jumps, e.g. impulsive maneuvers executing on any of the two satellites. The nonlinear analytical solution for propagating the first two moments and the probability density function are formulated by combining the STTs with a Gaussian mixture model. Numerical results show that the proposed method outperforms the linear covariance method and provides good agreement with Monte Carlo simulations on nonlinear, non-Gaussian uncertainty propagation. Moreover, as the STTs can be analytically computed and account for the J2-perturbation, the proposed uncertainty propagator is computationally efficient, which will be potentially useful for onboard conjunction analysis in satellites formulation flying mission.

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Section: F Summary and Discussionmentioning

confidence: 99%

Section: Stts For Relative State In J2-perturbed Elliptic Orbitsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear Analytical Uncertainty Propagation for Relative Motion near J2-Perturbed Elliptic Orbits

Yang

Luo

Lappas

et al. 2018

Journal of Guidance, Control, and Dynamics

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“…To maintain the relative position of satellites is to be hold in a certain formation geometry among the group of satellites Although, aerodynamic forces are being a negative effect, it can be actuating the aerodynamic panel by using the drag for station keeping. Herewith, streamlined linearized dynamic model is developed for better understanding of both J2 and atmospheric forces as well as formulation of stability analysis (Biria et al, 2016). The mission data has been configured through MATLAB/Simulink and obtained the numerical results are validate with real-time mission application.…”

Section: Introductionmentioning

confidence: 99%

Study the Influence of Atmospheric Drag and J2 Effect in a Close-proximity Operation at LEO

Sanjeeviraja¹,

Santhanakrishnan²,

Lakshmi³

2018

IJET

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In this paper is to assess the mission stability and the influence of J2 effect and aerodynamic forces. To maintain the relative motion of satellites by using a feedback control law for tracking error bound in the presence of J2 perturbation. A constant relative orbit under the effect of earth oblateness and conservative forces is referred as J2 and targeting the presence of atmospheric drag. Although, Schweighart and Sedwick control strategy for satellite relative motion is considering both lift and drag forces. The simulation result shows a better performance with high accuracy than an elliptical orbit under J2 perturbation and atmospheric drag along in-track formation. The algorithm and control strategies is useful tools for analysing a future space mission.

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A Survey of Relative Motion Dynamics and Control of Distributed Satellite Formation

Liu¹,

Wang

Huo³

et al. 2023

Lecture Notes in Electrical Engineering

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A satellite relative motion model including $$J_2$$ and $$J_3$$ via Vinti’s intermediary

Cited by 16 publications

References 44 publications

Nonlinear Analytical Uncertainty Propagation for Relative Motion near J2-Perturbed Elliptic Orbits

Nonlinear Analytical Uncertainty Propagation for Relative Motion near J2-Perturbed Elliptic Orbits

Study the Influence of Atmospheric Drag and J2 Effect in a Close-proximity Operation at LEO

A Survey of Relative Motion Dynamics and Control of Distributed Satellite Formation

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