The Cluster Orbits With Perturbations of Keplerian Elements (COWPOKE) Equations

McLaughlin, Craig; Luu, Kim

doi:10.21236/ada424880

Cited by 6 publications

(8 citation statements)

References 6 publications

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“…(10) and (11). It might be tempting to assume that P 2body and V 2body occur independently of one another, but they are coupled.…”

Section: Test Formationsmentioning

confidence: 99%

“…This is due to a lack of symmetry in the cross-track motion of D1 and D2 that is not captured by Eqs. (10) and (11). When Eqs.…”

Section: In-track/cross-track Test Formationmentioning

confidence: 99%

“…When Eqs. (10) and (11) are used the magnitude of the cross-track position and velocity of D1 and D2 are equal at every instant in time. This, however, is not realistic because D1 is ahead of D2 in its orbit.…”

Section: In-track/cross-track Test Formationmentioning

confidence: 99%

“…This section evaluates the effects of unmodeled perturbations on the accuracy of Eqs. (10) and (11). Perturbations can cause significant secular drifts in the separation between vehicles that cause the desired formation geometry to degrade over time.…”

Section: Evaluation Of Test Formations In Perturbed Orbitsmentioning

confidence: 99%

“…This dependence shows up as a direct result of the use of true anomaly as the independent variable. Sabol et al 11 derived a solution similar to that of Garrison et al, 9 but incorporated a Fourier-Bessel expansion of the true anomaly in terms of the mean anomaly and eccentricity. The expansion is cumbersome, particularly for high eccentricity cases.…”

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confidence: 99%

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Formation Design in Eccentric Orbits Using Linearized Equations of Relative Motion

Lane

Axelrad

2006

Journal of Guidance, Control, and Dynamics

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Geometrical methods for formation flying design based on the analytical solution to Hill's equations have been previously developed and used to specify desired relative motions in near circular orbits. These approaches offer valuable insight into the relative motion and allow for the rapid design of satellite configurations to achieve mission specific requirements, such as vehicle separation at perigee or apogee, minimum separation, or a particular geometrical shape. A comparable set of geometrical relationships for formations in eccentric orbits, where Hill's equations are not valid, is presented. The use of these relationships to investigate formation designs and their evolution in time is demonstrated. Nomenclature A= amplitude parameter a = semimajor axis C = unit vector in cross-track directon E = eccentric anomaly e = eccentricity I = unit vector in in-track direction i = inclination M = mean anomaly n = mean motion P = magnitude of position error R = unit vector in radial direction r = magnitude of r r = Earth-centered-inertial (ECI) position vector S = sensitivity matrix T = transformation matrix from ECI coordinates to RIC coordinates t = time V = magnitude of velocity error v = ECI velocity vector W e = rotation rate of Earth, 7.2921158553 × 10 −5 rad/s x = radial position distance from origin of radial, in-track, cross-track (RIC) frame y = in-track position distance from origin of RIC frame z = cross-track position distance from origin of RIC frame α = generic orbital element, for example, a, e, i, , ω, or M 0 γ = phase angle in in-track/cross-track plane α = small perturbation in α θ = argument of latitude µ = gravitational parameter of Earth, 3.986004418 × 10 14 m 3 /s 2 ν = true anomaly ξ = cross-track angular separation ρ = distance between two points in RIC frame ϕ = in-track angular separation ψ = phase parameter = right ascension of ascending node ω = argument of perigee

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“…(10) and (11). It might be tempting to assume that P 2body and V 2body occur independently of one another, but they are coupled.…”

Section: Test Formationsmentioning

confidence: 99%

“…This is due to a lack of symmetry in the cross-track motion of D1 and D2 that is not captured by Eqs. (10) and (11). When Eqs.…”

Section: In-track/cross-track Test Formationmentioning

confidence: 99%