f w g c [ 3 3 Cin ( tr c f F T F ( in o th o c f D frequency (LF we present the good correspon confirming the 26]). 3. NONLINEA 3.1 Global and Compared to li nitial condition (`perturbed') by ransient resona can result in dra frequency-ener Fig. 4 Two dif To construct th FEP is in the ba (conserved) ene ndicating the i oscillating with he NES. Unsy orbit on branc countable infin frequency-ener DOF system w and HF) comp corresponding ndence betwee previous theor AR SYSTEM I d Local Issues inear modal an ns-dependent, y nonlinear co ance capture o astically differ rgy plot (FEP [ fferent damped captur he Hamiltonian ackground in th ergy. Symmetr internal resona h identical dom ymmetric perio ches Snm an nity of period rgy dependence ould possess a ponents of the L g slow compon en the analytic retical argumen IDENTIFICA nalysis, NSI of so that even t orrections mig of the strongly rent transient dy 31]), which pro d nonlinear tr e; (right) tran n FEP for syste he first row of ric periodic orb ance (e.g., a 1 minant frequenc dic orbits Upq nd Unm is dic orbits. Nea e), whereas cur FEP with just LO and the NE nents in the co cal and numer nts (for additio ATION f dynamical sys the simple task ght be an over nonlinear syst ynamics. To il ovides a globa ransitions of sy nsition with ze em (5) we set f Fig. 4, where bits Snm cor :1 internal res cies). The ( ) qare Lissajou given by FI ar-horizontal b rved branches i two horizonta ES derived by s omplex plane ( rical results fo onal application stems is far mo k of identifyin rsimplification tem (5) we sho lustrate this po al picture of the ystem (5) depi ero initial cond 1 2 0 an a frequency in rrespond to cur sonance is real ) signs indicate us curves in th 0 / n m . Th branches are l imply strongly l lines correspo slow flow anal (which incorpo or these two d ns we refer to more complex. N ng a set of (lin of the proble ould recognize oint we introdu e dynamics. icted in the FE ditions but (y nd compute its ndex (FI) of a p rves in the con lized on 11 S e in-phase or o he configuration he (seemingly linearized or y nonlinear resp onding to its na lysis and EMD orates phase in dominant com Lee et al. [25] Nonlinear syst nearized) moda em. Using as e that a change uce in our discu EP: (left) 1:3 t (0) 0.579 periodic orbit periodic orbit i nfiguration plan , with both th out-of-phase mo n plane. Then, y simple) syst weakly nonlin ponses (the cor atural frequenc D; in the right c nformation). Th mponents (cf. F and Tsakirtzis tems are energ al matrices mo an example th e in initial cond ussion the conc transient reso ts [51]. The res s depicted agai ne ( , ) y v , with he LO and the otions of the L , the FI of a pe tem (5) posse near motions rresponding lin cies). olumn, here is Fig. 1) s et al. y- and odified he 1:3 ditions cept of nance sulting inst its h : m n , e NES LO and eriodic sses a (weak near 2518
RkJQdWJsaXNoZXIy MTMzNzEzMQ==