InthispaperanapproximateequationisderivedtodescribesmoothpartsofthestabilityboundaryforlinearHamiltoniansystems,dependingonarbitrarynumberofparameters.Withthisequation,wecanobtainparameterscorrespondingtothestabilityboundary,aswellastothestabilityandinstabilitydomains,pro-videdthatonepointonthestabilityboundaryisknown.Thendifferentialequationsdescribingtheevolutionofeigenvaluesandeigenvectorsalongacurveonthesta-bilityboundarysurfacearederived.Theseequationsalsoallowustoobtaincurvesbelongingtothestabilityboundary.Applicationstolineargyroscopicsystemsareconsideredandstudiedwithexamples.
