On the construction of periodic solutions of a nonautonomous quasilinear system with two degrees of freedom

1963 ◽  
Vol 27 (2) ◽  
pp. 544-550
Author(s):  
G.V. Plotnikova
Keyword(s):  
Periodic Solutions ◽  
Degrees Of Freedom ◽  
Quasilinear System ◽  
Two Degrees Of Freedom

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.

Detection of Periodic Orbits in Hamiltonian Systems Using Lagrangian Descriptors

2017 ◽  
Vol 27 (14) ◽  
pp. 1750225 ◽  
Author(s):  
Atanasiu Stefan Demian ◽  
Stephen Wiggins
Keyword(s):  
Phase Space ◽  
Periodic Solutions ◽  
Periodic Orbits ◽  
Hamiltonian Systems ◽  
Degrees Of Freedom ◽  
Space Structure ◽  
Two Degrees Of Freedom ◽  
Phase Space Structure ◽  
Lyapunov Orbits ◽  
Lagrangian Descriptors

The purpose of this paper is to apply Lagrangian Descriptors, a concept used to describe phase space structure, to autonomous Hamiltonian systems with two degrees of freedom in order to detect periodic solutions. We propose a method for Hamiltonian systems with saddle-center equilibrium and apply this approach to the classical Hénon–Heiles system. The method was successful in locating the unstable Lyapunov orbits in phase space.

scholarly journals VII.—On the Adelphic Integral of the Differential Equations of Dynamics

1918 ◽  
Vol 37 ◽  
pp. 95-116 ◽  
Author(s):  
E. T. Whittaker
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Two Degrees Of Freedom ◽  
Image Position ◽  
Kinetic And Potential Energies

§ 1. Ordinary and singular periodic solutions of a dynamical system. — The present paper is concerned with the motion of dynamical systems which possess an integral of energy. To fix ideas, we shall suppose that the system has two degrees of freedom, so that the equations of motion in generalised co-ordinates may be written in Hamilton's formwhere (q1q2) are the generalised co-ordinates, (p1, p2) are the generalised momenta, and where H is a function of (q1, q2, p1, p2) which represents the sum of the kinetic and potential energies.

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