Extension of Floquet's theory to nonlinear periodic differential systems and embedding diffeomorphisms in differential flows

2002 ◽  
Vol 124 (1) ◽  
pp. 107-127 ◽  
Author(s):  
Weigu Li ◽  
Jaume Llibre ◽  
Xiang Zhang
Keyword(s):  
Differential Systems ◽  
Floquet’S Theory ◽  
Floquet's Theory

Epicyclic Gear Vibrations

1976 ◽  
Vol 98 (3) ◽  
pp. 811-815 ◽  
Author(s):  
M. Botman
Keyword(s):  
Natural Frequencies ◽  
Gear Tooth ◽  
Planetary Gear ◽  
Periodic Coefficients ◽  
Plane Vibration ◽  
Epicyclic Gear ◽  
Floquet’S Theory ◽  
Floquet's Theory

The natural frequenices of in-plane vibration of a single planetary gear stage are analyzed. The gear tooth stiffnesses are approximated as linear springs. The effect of planet pin stiffness on the natural frequencies is evaluated. Rotation of the carrier gives rise to a system with periodic coefficients which is solved by means of Floquet’s theory. The rotation of the carrier appears to suppress the nonaxisymmetric modes which are present in the system with nonrotating carrier.

On the Stability Behavor of Bifurcated Normal Modes in Coupled Nonlinear Systems

1989 ◽  
Vol 56 (1) ◽  
pp. 155-161 ◽  
Author(s):  
C. H. Pak
Keyword(s):  
Nonlinear Systems ◽  
Calculus Of Variations ◽  
Normal Modes ◽  
Nonlinear Oscillators ◽  
Coupled Nonlinear Oscillators ◽  
Floquet’S Theory ◽  
Generic Bifurcation ◽  
The Stability ◽  
Floquet's Theory

The stability of bifurcated normal modes in coupled nonlinear oscillators is investigated, based on Synge’s stability in the kinematico-statical sense, utilizing the calculus of variations and Floquet’s theory. It is found, in general, that in a generic bifurcation, the stabilities of two bifurcated modes are opposite, and in a nongeneric bifurcation, the stability of continuing modes is opposite to that of the existing mode, and the stabilities of the two bifurcated modes are equal but opposite to that of the continuing mode. Some examples are illustrated.

LYAPUNOV VECTORS TREATMENT FOR BIFURCATIONS IN RETARDED DIFFERENTIAL SYSTEMS

1988 ◽  
Vol 49 (C2) ◽  
pp. C2-389-C2-392 ◽  
Author(s):  
M. LE BERRE ◽  
E. RESSAYRE ◽  
A. TALLET ◽  
J. J. ZONDY
Keyword(s):  
Differential Systems
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