On the construction of periodic solutions of a nonautonomous quasi-linear system with two degrees of freedom

1960 ◽  
Vol 24 (5) ◽  
pp. 1408-1415 ◽  
Author(s):  
G.V Plotnikova
Keyword(s):  
Linear System ◽  
Periodic Solutions ◽  
Degrees Of Freedom ◽  
Two Degrees Of Freedom ◽  
Quasi Linear System

scholarly journals Periodic solutions of a nonlinear oscillatory system with two degrees of freedom

2005 ◽  
Vol 47 (2) ◽  
pp. 249-263
Author(s):  
Zhengqiu Zhang ◽  
Yusen Zhu ◽  
Biwen Li
Keyword(s):  
Periodic Solutions ◽  
Degrees Of Freedom ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Oscillatory System ◽  
Continuation Theorem ◽  
Two Degrees Of Freedom ◽  
Nonlinear Oscillatory System ◽  
Existence Of Periodic Solutions

AbstractWe study a nonlinear oscillatory system with two degrees of freedom. By using the continuation theorem of coincidence degree theory, some sufficient conditions are obtained to establish the existence of periodic solutions of the system.

Inertially Coupled Galloping of Iced Conductors

1992 ◽  
Vol 59 (1) ◽  
pp. 140-145 ◽  
Author(s):  
P. Yu ◽  
A. H. Shah ◽  
N. Popplewell
Keyword(s):  
Periodic Solutions ◽  
Cross Section ◽  
Mixed Mode ◽  
Bifurcation Theory ◽  
Degrees Of Freedom ◽  
Center Of Mass ◽  
Asymptotic Solutions ◽  
Periodic Motions ◽  
Two Degrees Of Freedom ◽  
First Time

This paper is concerned with the galloping of iced conductors modeled as a two-degrees-of-freedom system. It is assumed that a realistic cross-section of a conductor has eccentricity; that is, its center of mass and elastic axis do not coincide. Bifurcation theory leads to explicit asymptotic solutions not only for the periodic solutions but also for the nonresonant, quasi-periodic motions. Critical boundaries, where bifurcations occur, are described explicitly for the first time. It is shown that an interesting mixed-mode phenomenon, which cannot happen in cocentric cases, may exist even for nonresonance.

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