Calibration of Linearized Solutions for Satellite Relative Motion

Sinclair, Andrew J.; Sherrill, Ryan E.; Lovell, T. Alan

doi:10.2514/1.g000037

Cited by 17 publications

(14 citation statements)

References 9 publications

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“…The proposed approach makes use of the results of Sinclair et al (2014), which show that the linearized relative dynamics described either in the local Cartesian frame or through orbital elements differences share an equivalence through a linearized transformation. In this frame, Sinclair et al (2014) propose a method to calibrate the initial conditions for the linearized Cartesian equations of motion, to reduce the linearization error that occurs when employing initial conditions purely calculated from kinematics.…”

Section: From Cartesian To Roes-based Modelsmentioning

confidence: 99%

“…In this frame, Sinclair et al (2014) propose a method to calibrate the initial conditions for the linearized Cartesian equations of motion, to reduce the linearization error that occurs when employing initial conditions purely calculated from kinematics. Such calibration consists in mapping linearly the orbital elements differences into the Cartesian relative state x through the matrix developed by Schaub and Junkins (2003, pp.…”

Section: From Cartesian To Roes-based Modelsmentioning

confidence: 99%

“…-A framework for transferring the available results in the local Cartesian frame into our ROE-based environment has been defined. It is based on the equivalence that the linearized dynamics expressed either in the local Cartesian frame or through differences of orbital elements share (Sinclair et al 2014). Afterwards, the linear relations developed in D' Amico (2005) are used for mapping ROEs into the Cartesian frame and vice versa.…”

Section: Introductionmentioning

confidence: 99%

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Model of $$J_2$$ J 2 perturbed satellite relative motion with time-varying differential drag

Gaias

Ardaens

Montenbruck

2015

Celest Mech Dyn Astr

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This work revisits the modeling of the relative motion between satellites flying in near-circular low-Earth-orbits. The motion is described through relative orbital elements and both Earth's oblateness and differential drag perturbations are addressed. With respect to the former formulation, the description of the J 2 effect is improved by including also the changes that this perturbation produces in both relative mean longitude and relative inclination vector during a drifting phase, when a non-vanishing relative semi-major axis is required. The second major improvement consists in a general empirical formulation to include the mean effects produced by non-conservative perturbations, such as the differential aerodynamic drag acceleration. As a result, in addition to the well-known actions on the relative semi-major axis and on the mean along-track separation, the model is able to reflect the mean variation of the relative eccentricity vector due to atmospheric density oscillations produced by day and night transitions.

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Section: From Cartesian To Roes-based Modelsmentioning

confidence: 99%

Section: From Cartesian To Roes-based Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Model of $$J_2$$ J 2 perturbed satellite relative motion with time-varying differential drag

Gaias

Ardaens

Montenbruck

2015

Celest Mech Dyn Astr

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“…Accordingly, some researchers additionally seek to harmonize these two types of models [11,21]. For example, Sengupta and Vadali [11] have revealed that a linear relationship between the constants of integration of the TH equations and the differential orbital elements exists.…”

Section: Introductionmentioning

confidence: 99%

“…Relative motion equations for circular or elliptic reference orbits by using differential orbital elements have been discussed in Refs. [12][13][14][15][16][17][18][19][20][21]. Garrison et al [12] firstly obtained the orbital elementbased relative motion equations by using a geometric approach.…”

Section: Introductionmentioning

confidence: 99%

Linearized relative motion equations through orbital element differences for general Keplerian orbits

Dang

Zhang

2018

Astrodyn

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A new formulation of the orbital element-based relative motion equations is developed for general Keplerian orbits. This new solution is derived by performing a Taylor expansion on the Cartesian coordinates in the rotating frame with respect to the orbital elements. The resulted solution is expressed in terms of two different sets of orbital elements. The first one is the classical orbital elements and the second one is the nonsingular orbital elements. Among of them, however, the semi-latus rectum and true anomaly are used due to their generality, rather than the semi-major axis and mean anomaly that are used in most references. This specific selection for orbital elements yields a new solution that is universally applicable to elliptic, parabolic and hyperbolic orbits. It is shown that the new orbital element-based relative motion equations are equivalent to the Tschauner-Hempel equations. A linear map between the initial orbital element differences and the integration constants associated with the solution of the Tschauner-Hempel equations is constructed. Finally, the presented solution is validated through comparison with a high-fidelity numerical orbit propagator.The numerical results demonstrate that the new solution is computationally effective; and the result is able to match the accuracy that is required for linear propagation of spacecraft relative motion over a broad range of Keplerian orbits.

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Coordinate‐Invariant Linear Quadratic Control

Burnett

Sinclair

Butcher

2019

Proc Appl Math and Mech

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This paper shows how the linear quadratic regulator (LQR) designs in different coordinate choices are related. Given the LQR design in one coordinate choice, it is shown that the LQR design for an alternate coordinate choice can be recovered through use of the nonlinear and linearized coordinate transformations. This provides the analyst a method of comparing coordinate choices that is more straightforward than previously suggested methods involving nonlinearity indices.

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Calibration of Linearized Solutions for Satellite Relative Motion

Cited by 17 publications

References 9 publications

Model of $$J_2$$ J 2 perturbed satellite relative motion with time-varying differential drag

Model of $$J_2$$ J 2 perturbed satellite relative motion with time-varying differential drag

Linearized relative motion equations through orbital element differences for general Keplerian orbits

Coordinate‐Invariant Linear Quadratic Control

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