Fuel Efficiency of Fully and Underconstrained Coulomb Formations in Slightly Elliptic Reference Orbits

Memon, M. Wasif; Nazari, Morad; Seo, Dongeun; Butcher, Eric A.

doi:10.1109/taes.2021.3090920

Cited by 2 publications

(4 citation statements)

References 22 publications

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“…However, this does not meet the necessary condition for one-dimensional torus, which means that the m : n-period orbit has no linear solution. Further considering the nonlinear term in (18) and the symmetry of sine and cosine functions, the analytical solution around the equilibrium can be expanded in the power series as…”

Section: : N-periodic Orbitsmentioning

confidence: 99%

“…. By substituting this linear solution into (18), the coefficients of the second-order solution can be solved using the Lindstedt-Poincaré method. Similarly, when the coefficients up to order N − 1 are obtained, i.e., x(t), y(t), and z(t) are determined up to order N − 1, ω and ∆ are determined up to order N − 2.…”

Section: : N-periodic Orbitsmentioning

confidence: 99%

“…To compute the N -order power series of m : n-period orbits, we should also analyze the composition of the N -order term on the left side of (18). Different from Lissajous orbits, the N -order unknown term of ∆z appears in m : nperiod orbits.…”

Section: : N-periodic Orbitsmentioning

confidence: 99%

“…Ref. [18] studied two different two-craft Coulomb formations in near-circular reference orbits. The Udwadia-Kalaba formulation is implemented to achieve and maintain the formation along the nadir direction and the formation with a constant separation distance.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

High-order analytical solutions of bounded relative motions for Coulomb formation flying

Lin

Zhang

et al. 2023

Nonlinear Dyn

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Close-proximity Coulomb formation flying offers attractive prospects in multiple astronautical missions. An analytical method of constructing the series solution up to an arbitrary order for the relative motion near the equilibrium of Coulomb formation systems is proposed to facilitate the design of Coulomb formations based on a Lindstedt-Poincaré method. The details of the series expansion and coefficient solution for Lissajous orbits and arbitrary m : n-period orbits are discussed. To verify the effectiveness of the Lindstedt-Poincaré method in constructing series solutions, the practical convergence domain of series solutions for various bounded orbits is computed by comparison with the corresponding exact numerical solutions. Given the accuracy requirements of practical formation missions, the configuration design for the Coulomb formation can be carried out conveniently and quickly by employing the proposed series solutions.

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Section: : N-periodic Orbitsmentioning

confidence: 99%

Section: : N-periodic Orbitsmentioning

confidence: 99%

Section: : N-periodic Orbitsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

High-order analytical solutions of bounded relative motions for Coulomb formation flying

Lin

Zhang

et al. 2023

Nonlinear Dyn

View full text Add to dashboard Cite

show abstract

High-order analytical solutions of bounded relative motions for Coulomb formation flying

Lin¹,

Zhang²,

et al. 2022

Preprint

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Close-proximity Coulomb formation flying offers attractive prospects in multiple astronautical missions. An analytical method of constructing the series solution up to an arbitrary order for the relative motion near the equi-librium of Coulomb formation systems is proposed to facilitate the design of Coulomb formations based on a Lindstedt-Poincaré method. The details of the series expansion and coeﬀicient solution for Lissajous orbits and arbitrary m : n-period orbits are discussed. To verify the effectiveness of the Lindstedt-Poincaré method in constructing series solutions, the practical convergence domain of series solutions for various bounded orbits is computed by com-parison with the corresponding exact numerical solutions. Given the accuracy requirements of practical formation missions, the configuration design for the Coulomb formation can be carried out conveniently and quickly by employing the proposed series solutions.

show abstract

Fuel Efficiency of Fully and Underconstrained Coulomb Formations in Slightly Elliptic Reference Orbits

Cited by 2 publications

References 22 publications

High-order analytical solutions of bounded relative motions for Coulomb formation flying

High-order analytical solutions of bounded relative motions for Coulomb formation flying

High-order analytical solutions of bounded relative motions for Coulomb formation flying

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