简介：Displacednon-Keplerianorbitsaboveplanetarybodiescanbeachievedbyorientatingthesolarsailnormaltothesunline.ThedynamicalsystemstechniquesareemployedtoanalyzethenonlineardynamicsofadisplacedorbitanddifferenttopologiesofequilibriaareyieldedfromthebasicconfigurationsofHill'sregion,whichhaveasaddlenodebifurcationpointatthedegeneratedcase.Thesolarsailnearhyperbolicordegeneratedequilibriumisquiteunstable.Therefore,acontrollerpreservingHamiltonianstructureispresentedtostabilizethesolarsailnearhyperbolicordegeneratedequilibrium,andtogeneratethestableLissajousorbitsthatstaystableinsidethestabilizingregionofthecontroller.ThemaincontributionofthispaperisthatthecontrollerpreservingHamiltonianstructurenotonlychangestheinstabilityoftheequilibrium,butalsomakesthemodifiedellipticequilibriumbecomeuniqueforthecontrolledsystem.Theallocationlawofthecontrolleronthesail'sattitudeandlightnessnumberisobtained,whichverifiesthatthecontrollerisrealizable.