ISSN:
1573-269X
Schlagwort(e):
normal forms
;
time-periodic systems
;
Liapunov–Floquet transformation
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
Notizen:
Abstract The structure of time-dependent resonances arising in themethod of time-dependent normal forms (TDNF) for one andtwo-degrees-of-freedom nonlinear systems with time-periodic coefficientsis investigated. For this purpose, the Liapunov–Floquet (L–F)transformation is employed to transform the periodic variationalequations into an equivalent form in which the linear system matrix istime-invariant. Both quadratic and cubic nonlinearities are investigatedand the associated normal forms are presented. Also, higher-orderresonances for the single-degree-of-freedom case are discussed. It isdemonstrated that resonances occur when the values of the Floquet multipliers result in MT-periodic (M = 1, 2,...) solutions. The discussion is limited to the Hamiltonian case (which encompasses allpossible resonances for one-degree-of-freedom). Furthermore, it is alsoshown how a recent symbolic algorithm for computing stability andbifurcation boundaries for time-periodic systems may also be employed tocompute the time-dependent resonance sets of zero measure in theparameter space. Unlike classical asymptotic techniques, this method isfree from any small parameter restriction on the time-periodic term inthe computation of the resonance sets. Two illustrative examples (oneand two-degrees-of-freedom) are included.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1023/A:1008312424551
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