Mathematical Methods Applied to the Celestial Mechanics of Artificial Satellites 2013

226 Pages·2013·49.99 MB·English

Mathematical Problems in Engineering
Mathematical Methods Applied to
the Celestial Mechanics of
Artificial Satellites 2013
Guest Editors: Antonio F. Bertachini A. Prado, Josep J. Masdemont,
Maria Cecilia Zanardi, Silvia Maria Giuliatti Winter, Tadashi Yokoyama,
and Vivian Martins Gomes
Mathematical Methods Applied to the
Celestial Mechanics of Artificial Satellites 2013
Mathematical Problems in Engineering
Mathematical Methods Applied to the
Celestial Mechanics of Artificial Satellites 2013
Guest Editors: Antonio F. Bertachini A. Prado,
Josep J. Masdemont, Maria Cecilia Zanardi,
Silvia Maria Giuliatti Winter, Tadashi Yokoyama,
and Vivian Martins Gomes
Copyright©2013HindawiPublishingCorporation.Allrightsreserved.
Thisisaspecialissuepublishedin“MathematicalProblemsinEngineering.”Allarticlesareopenaccessarticlesdistributedunderthe
CreativeCommonsAttributionLicense,whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedthe
originalworkisproperlycited.
Editorial Board
M.AbdElAziz,Egypt ElmetwallyElabbasy,Egypt Ren-JiehKuo,Taiwan
E.M.Abdel-Rahman,Canada A.El´ıas-Zu´n˜iga,Mexico JurgenKurths,Germany
R.K.AbuAl-Rub,USA AndersEriksson,Sweden ClaudeLamarque,France
SarpAdali,SouthAfrica VedatS.Erturk,Turkey UsikLee,Korea
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ErweiBai,USA ZoranGajic,USA MingLi,China
EzzatG.Bakhoum,USA UgoGalvanetto,Italy JianLi,China
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C.Be´renguer,France BehrouzGatmiri,Iran PanosLiatsis,UK
JonathanN.Blakely,USA OlegV.Gendelman,Israel ShueeiM.Lin,Taiwan
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M.Boutayeb,France FabrizioGreco,Italy WanquanLiu,Australia
MichaelJ.Brennan,UK QuangPhucHa,Australia BinLiu,Australia
SalvatoreCaddemi,Italy M.R.Hajj,USA PaoloLonetti,Italy
PiermarcoCannarsa,Italy TonyS.W.Hann,Taiwan V.C.Loukopoulos,Greece
JoseE.Capilla,Spain ThomasHanne,Switzerland JunguoLu,China
CarloCattani,Italy K.R.(Stevanovic)Hedrih,Serbia Chien-YuLu,Taiwan
MarceloM.Cavalcanti,Brazil M.I.Herreros,Spain AlexeiMailybaev,Brazil
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MohammedChadli,France JaromirHoracek,CzechRepublic O.D.Makinde,SouthAfrica
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MichaelJ.Chappell,UK GordonHuang,Canada RoderickMelnik,Canada
KuiFuChen,China YiFengHung,Taiwan XinzhuMeng,China
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Jyh-HorngChou,Taiwan AnuarIshak,Malaysia EbrahimMomoniat,SouthAfrica
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SeppoPohjolainen,Finland ChengShao,China MoranWang,China
StanislavPotapenko,Canada BoShen,Germany YijingWang,China
SergioPreidikman,USA Jian-JunShu,Singapore Gerhard-WilhelmWeber,Turkey
CarstenProppe,Germany ZhanShu,UK J.A.S.Witteveen,TheNetherlands
HectorPuebla,Mexico DanSimon,USA Kwok-WoWong,HongKong
JustoPuerto,Spain LucianoSimoni,Italy LigangWu,China
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GianlucaRanzi,Australia DavideSpinello,Canada WangXing-yuan,China
SivaguruRavindran,USA SriSridharan,USA XiFrankXu,USA
G.Rega,Italy RolfStenberg,Finland XupingXu,USA
PedroRibeiro,Portugal ChangyinSun,China Jun-JuhYan,Taiwan
J.Rodellar,Spain JitaoSun,China Xing-GangYan,UK
R.Rodriguez-Lopez,Spain Xi-MingSun,China Suh-YuhYang,Taiwan
A.J.Rodriguez-Luis,Spain AndrzejSwierniak,Poland MahmoudT.Yassen,Egypt
IgnacioRomero,Spain YangTang,Germany MohammadI.Younis,USA
HamidRonagh,Australia AllenTannenbaum,USA BoYu,China
CarlaRoque,Portugal CristianToma,Romania HuangYuan,Germany
Rube´nR.Garc´ıa,Spain IrinaN.Trendafilova,UK S.P.Yung,HongKong
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IlmarF.Santos,Denmark K.Vajravelu,USA JianmingZhan,China
NickolasS.Sapidis,Greece VictoriaVampa,Argentina XuZhang,China
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BozidarSarler,Slovenia StefanoVidoli,Italy LuZhen,China
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A.P.Seyranian,Russia YongqiWang,Germany MustaphaZidi,France
LeonidShaikhet,Ukraine ChengC.Wang,Taiwan
Contents
MathematicalMethodsAppliedtotheCelestialMechanicsofArtificialSatellites2013,
AntonioF.BertachiniA.Prado,JosepJ.Masdemont,MariaCeciliaZanardi,SilviaMariaGiuliattiWinter,
TadashiYokoyama,andVivianMartinsGomes
Volume2013,ArticleID854317,5pages
FaultDetectionandIsolationinInertialMeasurementUnitsBasedon𝜒2-CUSUMandWaveletPacket,
E´lcioJeronimodeOliveira,IjarMilagredaFonseca,andHe´lioKoitiKuga
Volume2013,ArticleID869293,10pages
AttitudeDynamicsandStabilityofaSimpleSolarPhotonThruster,AnnaD.Guerman,GeorgiSmirnov,
andMariaCeciliaPereira
Volume2013,ArticleID943107,7pages
StudyingCloseApproachesforaCloudofParticlesConsideringAtmosphericDrag,VivianMartins
Gomes,JorgeFormiga,andRodolphoVilhenadeMoraes
Volume2013,ArticleID468624,10pages
DesignoftheMicrosatelliteAttitudeControlSystemUsingtheMixed𝐻 /𝐻 MethodviaLMI
2 ∞
Optimization,ErbersonRodriguesPinheiroandLuizCarlosGadelhadeSouza
Volume2013,ArticleID257193,8pages
AttitudeDeterminationwithMagnetometersandAccelerometerstoUseinSatelliteSimulator,
HelioKoitiKugaandValdemirCarrara
Volume2013,ArticleID401282,6pages
ApplicationoftheKalmanFiltertoEstimatetheStateofanAerobrakingManeuver,
WillerGomesdosSantos,He´lioKoitiKuga,andEvandroMarconiRocco
Volume2013,ArticleID234270,8pages
ASimplePerturbationAlgorithmforInvertingtheCartesiantoGeodeticTransformation,
JamesD.TurnerandTarekElgohary
Volume2013,ArticleID712729,5pages
AStudyofSingle-andDouble-AveragedSecond-OrderModelstoEvaluateThird-BodyPerturbation
ConsideringEllipticOrbitsforthePerturbingBody,R.C.Domingos,A.F.BertachinideAlmeidaPrado,
andR.VilhenadeMoraes
Volume2013,ArticleID260830,11pages
TrajectoryEstimationofAircraftinaDouble-SatellitePassivePositioningSystemwiththeAdjoint
Method,AnzhouCao,YanqiuGao,JicaiZhang,andXianqingLv
Volume2013,ArticleID502610,7pages
AveragingMethodsforDesignofSpacecraftHysteresisDamper,RicardoGama,
AnnaD.Guerman,AnaSeabra,andGeorgiV.Smirnov
Volume2013,ArticleID483457,7pages
EstimatingFrictionParametersinReactionWheelsforAttitudeControl,
ValdemirCarraraandHe´lioKoitiKuga
Volume2013,ArticleID249674,8pages
ANewCelestialNavigationMethodforSpacecraftonaGravityAssistTrajectory,NingXiaolin,
HuangPanpan,andFangJiancheng
Volume2013,ArticleID950675,8pages
TheStudyoftheAsymmetricMultipleEncountersProblemandItsApplicationtoObtainJupiter
GravityAssistedManeuvers,DenilsonPauloSouzadosSantos,
AntoˆnioFernandoBertachinideAlmeidaPrado,andEvandroMarconiRocco
Volume2013,ArticleID745637,12pages
TangentOrbitalRendezvousUsingLinearRelativeMotionwith𝐽2Perturbations,GangZhang,
DongzheWang,XibinCao,andZhaoweiSun
Volume2013,ArticleID531672,8pages
DiscreteModelReferenceAdaptiveControlforGimbalServosystemofControlMomentGyrowith
HarmonicDrive,BangchengHan,YanpengChen,HaitaoLi,andLianhuiYang
Volume2013,ArticleID897579,10pages
AveragingTesseralEffects:ClosedFormRelegationversusExpansionsofEllipticMotion,MartinLara,
JuanF.San-Juan,andLuisM.Lo´pez-Ochoa
Volume2013,ArticleID570127,11pages
CircularOrbitTargetCaptureUsingSpaceTether-NetSystem,GuangZhai,Jing-ruiZhang,
andZhangYao
Volume2013,ArticleID601482,11pages
PreciseAnalyticalComputationofFrozen-Eccentricity,LowEarthOrbitsinaTesseralPotential,
MartinLara,JuanF.San-Juan,andLuisM.Lo´pez-Ochoa
Volume2013,ArticleID191384,13pages
SearchingforOrbitswithMinimumFuelConsumptionforStation-KeepingManeuvers:An
ApplicationtoLunisolarPerturbations,AntonioFernandoBertachinideAlmeidaPrado
Volume2013,ArticleID415015,11pages
OnboardandReal-TimeArtificialSatelliteOrbitDeterminationUsingGPS,
AnaPaulaMarinsChiaradia,He´lioKoitiKuga,andAntonioFernandoBertachinideAlmeidaPrado
Volume2013,ArticleID530516,8pages
MinimumFuelLow-ThrustTransfersforSatellitesUsingaPermanentMagnetHallThruster,
ThaisCarneiroOliveira,EvandroMarconiRocco,Jose´LeonardoFerreira,andAntonioF.B.A.Prado
Volume2013,ArticleID945030,12pages
DynamicsofArtificialSatellitesaroundEuropa,JeanPaulodosSantosCarvalho,
RodolphoVilhenadeMoraes,andAntoˆnioFernandoBertachinideAlmeidaPrado
Volume2013,ArticleID182079,7pages
StationKeepingofConstellationsUsingMultiobjectiveStrategies,EvandroMarconiRocco,
MarceloLopesdeOliveiraeSouza,andAntonioFernandoBertachinideAlmeidaPrado
Volume2013,ArticleID476451,15pages
HindawiPublishingCorporation
MathematicalProblemsinEngineering
Volume2013,ArticleID854317,5pages
http://dx.doi.org/10.1155/2013/854317
Editorial
Mathematical Methods Applied to the Celestial Mechanics
of Artificial Satellites 2013
AntonioF.BertachiniA.Prado,1JosepJ.Masdemont,2 MariaCeciliaZanardi,3
SilviaMariaGiuliattiWinter,3TadashiYokoyama,4andVivianMartinsGomes3
1INPE-DMC,AvenidadosAstronautas1758,12227-010Sa˜oJosedosCampos,SP,Brazil
2IEECandDepartamentdeMatema`ticaAplicadaI,UniversitatPolite`cnicadeCatalunya,Diagonal647,08028Barcelona,Spain
3UniversidadeEstadualPaulista,UNESP,CEP12516-410,CampusdeGuaratingueta´,Guaratingueta´,SP,Brazil
4UniversidadeEstadualPaulista,UNESP,CaixaPostal178,CEP13500-970,CampusdeRioClaro,RioClaro,SP,Brazil
CorrespondenceshouldbeaddressedtoAntonioF.BertachiniA.Prado;[email protected]
Received13November2013;Accepted13November2013
Copyright©2013AntonioF.BertachiniA.Pradoetal. This is an open access article distributed under the Creative Commons
AttributionLicense,whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkis
properlycited.
Studies related to celestial mechanics have been made for satellitelaunchedfromtheEarthbytheformerSovietUnion
a long time. The observation of the sky showed the stars, in 1957, the Sputnik, many important steps were made. The
in particular for some of them, called “Planets” by the manlandedontheMoonin1969;thetwoVoyagerspacecraft
Greeks,thathaveaparticularmotionagainsttheotherstars. discoveredmanynewmoonsaroundthegiantplanetsJupiter,
Thoseobservationschallengedthemindsofthosetimesand Saturn, and Uranus in the 70’s and 80’s, also finding many
speculations appeared to try to explain those motions. This aspectsoftheplanetsthemselvesthatwouldnotbefoundby
was the beginning of the astronomy science and opened telescopesbasedontheEarth.
a particular field of study, focused on understanding the The combination of theory and practical observations
motion of the planets, moons, asteroids, comets and other alsoshowedtheexistenceofplanetarysystemsaroundother
celestial bodies. Several of the most important names in stars, the so called “exoplanets.” Soon “exomoons” around
history are related to this field, like Ptolomeus, Nicolaus those“exoplanets”willbefound.
Copernicus,GalileoGalilei,JohannesKepler,IsaacNewton, GoingbacktoourmotherEarth,people’slifehaschanged
AlbertEinsteinandothers,whohelpedtofindthephysical dramatically for better after the space research activities
lawsthatgovernthosemotions. started.Instantaneouscommunicationsbytelephone,televi-
More recently, the last few decades brought the combi- sion, and so forth are mostly based on satellites travelling
nation of this science with more practical applications in aroundtheEarthinstrategicorbitsspecifiedbymethodsused
the engineering field. This combination created the term inastrodynamics.Drivingacarinanewplaceisnolongeran
“Astrodynamics,”whichisusuallyconnectedtothestudyof adventure,afterthepopularizationofsmallandcheapdevices
the motion of space vehicles made to explore the regions thatreceiveinformationfromaconstellationofsatellites,like
of the space around the Earth and beyond. Of course, the theGPS,andcalculateitspositioninamap.Thediscoveriesof
physicallawsarethesameforcelestialbodiesorspacecraft; resourcesonEarthmayalsobenefitfromimagestakenfrom
itisjustaquestionofemphasizingoneorotheraspectsofthe space.Veryimportantactivities,likeweatherforecast,which
knowledge. contributesinagriculturalactivitiesandinthepredictionof
Althoughveryrecentintermsofhistory,thisnewcombi- naturaldisaster,alsorelyonsatellites.
nationofscienceandengineeringhasalreadymadeseveral Thisspecialissueisthethirdoneofthisjournaldedicated
important contributions to science. From the first artificial toproblemsrelatedtospaceresearch.Itcoverstopicsrelated
2 MathematicalProblemsinEngineering
tomissiondesignfromeveryperspective,likeorbitselection, motionequations,itisonlysuitablefortheshort-rangecase
attitude and orbit propagation, control of spacecraft, and betweentwospacecraft.
relatedtopics.Thisissuegivesspecialattentiontoapplications Anotherpaperofthistopicis“ApplicationoftheKalman
onthosefields,inordertobecomplementarytopublications filter to estimate the state of an aerobraking maneuver,” by
that are more focused on theoretical developments. It has W. G. dos Santos et al., that study an application of the
a total of twenty three papers, which are briefly described Kalman filter used to estimate the position and velocity of
below. a spacecraft that is performing an aerobraking maneuver
Five of them are concerned with the problems of opti- in the atmosphere of the Earth. Two examples are used:
mal maneuvers. One of them is “Searching for orbits with the maneuver made by the Hiten spacecraft and an aero
minimumfuelconsumptionforstation-keepingmaneuvers:An brakingofasatellitethatisinalowEarthorbit.Themodel
applicationtolunisolarperturbations,”byA.Prado.Itdevelops considersareferencetrajectoryandatrajectoryperturbedby
a criterion to map orbits with respect to the perturbations externalforcesandnonidealitiesofthesensorsandactuators.
receivedbythesatellite.Themethodisbasedontheintegral APIDcontrollerandpropulsivejetsareusedtomaneuverthe
oftheperturbingforcesoverthetime.Thisindexmeasures spacecraft.Theresultsshowcomparisonsusingandnotusing
the variation of velocity transferred to the spacecraft by theKalmanfilter,showingtheimportanceofitsapplication.
the perturbations. It is a characteristic of the orbit and the Another topic covered in this special issue is related to
dynamicalsystemconsideredanditdoesnotdependonthe the determination, simulation, and propagation of orbits of
engineorstation-keepingtechniquesused.Theresultsshow spacecraft. There are five papers related to this topic. One
theeffectsoftheperturbationsduetotheSunandtheMoon of them is “Onboard and real-time artificial satellite orbit
inspacecraftaroundtheEarth. determinationusingGPS”,byA.P.MChiaradiaetal.,which
Then, the paper “Station keeping of constellations using introducesanalgorithmfororbitdeterminationapplyingthe
multiobjective strategies,” by E. Rocco et al., studies how to extended Kalman Filter method. An analysis is performed
perform station keeping maneuvers in constellations. The toascertainanadequacyofthemodelingcomplexityversus
ideaistomakethosemaneuversundertwoconditions:low accuracy. The minimum set to estimate states to reach the
fuelconsumptionandatimeconstraint.Theseconditionsare level of accuracy of tens of meters is found to have at least
appliedtoallthemembersoftheconstellation,soastrategy theposition,velocity,anduserclockoffsetcomponents.The
is searched to consider the global optimization of those dynamicalmodelisassessedthroughseveraltests,covering
variables.Thisisamultiobjectiveproblem.Tofindasolution, the force model, the numerical integration scheme and the
strategies that minimize the fuel consumption considering step-sizecontrol,usingsimplifiedvariationalequations.The
the constraints on the duration of the maneuver are used. algorithm is tested with real-time data from a satellite with
Severalexamplesareshowntoexemplifythetechnique. a GPS receiver on board. The satellite orbit is estimated
The next paper of that set is “Minimum fuel low-thrust using the algorithm developed with good accuracy and
transfersforsatellitesusingaPermanentmagnethallthruster,” minimumcomputationalcost.Inthisprocedure,theposition
by T. Oliveira et al., that studies the problem of the orbital and velocity errors obtained along one day vary from 15 to
maneuvers required to accomplish the goals of a space 20mandfrom0.014to0.018m/s,respectively,withstandard
mission. In particular, the situation where it is necessary to deviations from 6 to 10m and from 0.006 to 0.008m/s,
minimizethefuelconsumptionissolved,inordertoincrease respectively.
thelifetimeofthesatellite.Thepaperhastwoparticulargoals: Another paper of this topic is “Precise analytical com-
to develop an algorithm that can find optimal trajectories putation of frozen-eccentricity, low Earth orbits in a tesseral
with continuous thrust that can be used in several types of potential”, by M. Lara et al., that considers the problem of
missionsandtakingintoaccountdifferentconstraintsatthe finding frozen orbits using a higher degree geopotential,
same time and to study the performance of the propulsion which takes into account the short-period effects of the
devices under development at the Universidade de Brasilia tesseralharmonics.Thisapproachcandescribethebehavior
to perform orbital maneuvers. It includes a study of the of elliptic frozen orbits in conditions where a model based
consequenceoftheerrorsofthethrustlevelofthesepieces on the 𝐽2-𝐽3 terms is not good enough. Using this model it
ofequipment. is possible to find low Earth orbits that show smaller long-
Then comes the paper by G. Zhang et al., “Tangent periodeffectsinlong-termpropagationsthanthoseobtained
orbital rendezvous using linear relative motion with 𝐽2 per- whenusingthezonalmodeldesign.
turbations,”thatdiscussestheshort-rangecoplanarproblem Alsointhistopicthereisthepaper“Dynamicsofartificial
for elliptic orbits. Three cases are analyzed with the first, satellites around Europa,” by J. P. dos S. Carvalho et al.,
the second, or both impulses being tangent. For a given that searched for stable orbits around Europa. The orbital
initial point, the first two problems can be transformed elements of an artificial satellite in orbit around Europaare
intofindingallrootsofasinglevariablefunctionaboutthe analyzed by developing the disturbing potential in a power
transfer time, which can be done by the secant method. series of the eccentricity and inclination of the satellite.
The bitangent rendezvous problem requires the same solu- This satellite is under the gravitational effects of Europa,
tions obtained by considering the initial coasting time. with its gravitational coefficients 𝐽2 and 𝐽3 and Jupiter. The
A numerical example for two coplanar elliptic orbits is Lagrangeplanetaryequationsarenumericallyintegratedand
given to verify the efficiency of these proposed techniques. theresultsshowthatintherangeofsemimajoraxisbetween
However, since this method is based on the linear relative 2000km and 3000km several polar orbits can survive for