Second-order state transition for relative motion near perturbed, elliptic orbits

DOI10.1007/s10569-006-9054-5zbMath1162.70023OpenAlexW2008665679MaRDI QIDQ861360

Kyle T. Alfriend, Srinivas R. Vadali, Prasenjit Sengupta

Publication date: 29 January 2007

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10569-006-9054-5

zbMATH Keywords

Formation flightNonlinear relative motionNonsingular elementsState transition

Mathematics Subject Classification ID

Celestial mechanics (70F15) Orbital mechanics (70M20)

Related Items (14)

The equations of relative motion in the orbital reference frame ⋮ Integrable approximation of \(J_2\)-perturbed relative orbits ⋮ Solutions and periodicity of satellite relative motion under even zonal harmonics perturbations ⋮ A satellite relative motion model including \(J_2\) and \(J_3\) via Vinti's intermediary ⋮ The theory of asynchronous relative motion. I: Time transformations and nonlinear corrections ⋮ Nonlinear analytic solution for perturbed relative motion using differential equinoctial elements ⋮ Modeling orbital relative motion to enable formation design from application requirements ⋮ Minimum control for spacecraft formations in a J2 perturbed environment ⋮ Collective control of spacecraft swarms for space exploration ⋮ A second-order solution to the two-point boundary value problem for rendezvous in eccentric orbits ⋮ The Lambert \(W\) function and solutions to Kepler's equation ⋮ Symmetry properties of states and costates in impulsive control systems ⋮ Relative motion of satellites exploiting the super-integrability of Kepler's problem ⋮ Frozen-anomaly transformation for the elliptic rendezvous problem

Cites Work

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• Satellite relative motion using differential equinoctial elements
• Canonical modelling of relative spacecraft motion via epicyclic orbital elements
• New form for the optimal rendezvous equations near a Keplerian orbit
• Fuel-optimal rendezvous near a point in general Keplerian orbit
• State Transition Matrices for Terminal Rendezvous Studies: Brief Survey and New Example
• An intelligent control concept for formation flying satellites
• Second-order solution to the elliptical rendezvous problem.
• On the equinoctial orbit elements
• Generalization of Lagrange's implicit function theorem to N-dimensions

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