Therearespin-orbitinteractionandspin-spininteractioninagenericpost-NewtonianLagrangianformulationofcomparablemassspinningcompactbinaries.Thespin-orbitcouplingorthespin-spincouplingplaysaquiteimportantroleinchangingtheevolutionofthesystemandmaysometimecausechaoticbehavior.Howdothetwotypesofcouplingsexerttogetheranyinfluencesonchaosinthisformulation?Toanswerit,wesimplytaketheLagrangianformulationofaspecialbinarysystem,includingtheNewtoniantermandtheleading-orderspin-orbitandspin-spincouplings.ThekeytothisquestioncanbefoundfromaHamiltonianformulationthatiscompletelyidenticaltotheLagrangianformulation.IftheLagrangiandoesnotincludethespin-spincoupling,itsequivalentHamiltonianhasanadditionalterm(i.e.thenext-orderspin-spincoupling)aswellasthosetermsoftheLagrangian.Thespin-spincouplingratherthanthespin-orbitcouplingmakestheHamiltoniantypicallynonintegrableandprobablychaoticwhentwoobjectsspin.Whentheleading-orderspin-spincouplingisalsoaddedtotheLagrangian,itstillappearsintheHamiltonian.Inthissense,thetotalHamiltoniancontainstheleading-orderspin-spincouplingandthenext-orderspin-spincoupling,whichhavedifferentsigns.Therefore,thechaosresultingfromthespin-spininteractionintheLegrangianformulationsissomewhatweakenedbythespin-orbitcoupling.
