Optimization of low-thrust limited-power trajectories in a noncentral gravity field-transfers between orbits with small eccentricities
type: Item
instance of: scholarly article
title: Optimization of low-thrust limited-power trajectories in a noncentral gravity field-transfers between orbits with small eccentricities
zbMATH Open document ID: 1331.70068
DOI: 10.1155/2009/503168
author: Sandro da Silva Fernandes
published in: Mathematical Problems in Engineering
publication date: 2009-11-13T00:00:00Z
review text: Summary: Numerical and first-order analytical results are presented for optimal low-thrust limited-power trajectories in a gravity field that includes the second zonal harmonic \(J_{2}\) in the gravitational potential. Only transfers between orbits with small eccentricities are considered. The optimization problem is formulated as a Mayer problem of optimal control with Cartesian elements-position and velocity vectors-as state variables. After applying the Pontryagin Maximum Principle, successive canonical transformations are performed and a suitable set of orbital elements is introduced. Hori method -- a perturbation technique based on Lie series -- is applied in solving the canonical system of differential equations that governs the optimal trajectories. First-order analytical solutions are presented for transfers between close orbits, and a numerical solution is obtained for transfers between arbitrary orbits by solving the two-point boundary value problem described by averaged maximum Hamiltonian, expressed in nonsingular elements, through a shooting method. A comparison between analytical and numerical results is presented for some maneuvers.
Mathematics Subject Classification ID: 70M20
Mathematics Subject Classification ID: 70Q05
Mathematics Subject Classification ID: 49N90
zbMATH DE Number: 5632494
Wikidata QID: Q58649016
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2009/503168
OpenAlex ID: W2090771157
cites work: Optimum low-thrust rendezvous and station keeping
cites work: Q3875412
cites work: Optimal low-thrust transfer between neighbouring quasi-circular orbits around an oblate planet
cites work: Optimal low-thrust limited power transfer between neighbouring quasi-circular orbits of small inclinations around an oblate planet
cites work: Trajectory Optimization Using Nonsingular Orbital Elements and True Longitude
cites work: Reformulation of Edelbaum's Low-Thrust Transfer Problem Using Optimal Control Theory
cites work: Optimal multi-objective low-thrust spacecraft trajectories
cites work: New challenges to trajectory design by the use of electric propulsion and other new means of wandering in the solar system
cites work: Optimal low-thrust orbital transfers in a central gravity field
cites work: Averaging and optimal control of elliptic keplerian orbits with low propulsion
cites work: Q3974046
cites work: Q3285814
cites work: Theory of satellite geodesy. Applications of satellites to geodesy.
cites work: Q4376870
cites work: Q4779819
Recommended article: Optimal low-thrust limited-power transfers in a non-central gravity field - transfers between arbitrary orbits
Recommended article: Optimal low-thrust transfers between coplanar orbits with small eccentricities
Recommended article: A numerical study for optimal low-thrust limited power transfers between coplanar orbits with small eccentricities
Recommended article: Optimal low-thrust orbital transfers in a central gravity field
Recommended article: Applied Nonsingular Astrodynamics
Recommended article: Q3651967
Recommended article: Numerical and analytical study of optimal low-thrust limited-power transfers between close circular coplanar orbits
Recommended article: An efficient computational approach to minimum-fuel low-thrust non-coplanar orbit transfer
Recommended article: A first-order analytical theory for optimal low-thrust limited-power transfers between arbitrary elliptical coplanar orbits
Recommended article: A numerical study of low-thrust limited power trajectories between coplanar circular orbits in an inverse-square force field
description: scientific article; zbMATH DE number 5632494