Analysis of Orbital Stability of Self-excited Periodic Motions in Lure System

2020 ◽  
pp. 177-196
Author(s):  
Igor Boiko
Keyword(s):  
Orbital Stability ◽  
Periodic Motions

On the orbital stability of planar periodic motions of a rigid body in the Bobylev-Steklov case

2012 ◽  
Vol 17 (6) ◽  
pp. 533-546 ◽  
Author(s):  
B. S. Bardin ◽  
T. V. Rudenko ◽  
A. A. Savin
Keyword(s):  
Rigid Body ◽  
Orbital Stability ◽  
Periodic Motions

scholarly journals On a Method of Introducing Local Coordinates in the Problem of the Orbital Stability of Planar Periodic Motions of a Rigid Body

2020 ◽  
Vol 16 (4) ◽  
pp. 581-594
Author(s):  
B.S. Bardin ◽  
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Orbital Stability ◽  
Hamiltonian Function ◽  
Periodic Motions ◽  
Autonomous Hamiltonian System ◽  
Change Of Variables ◽  
Heavy Rigid Body ◽  
Local Coordinates ◽  
Parameter Values

A method is presented of constructing a nonlinear canonical change of variables which makes it possible to introduce local coordinates in a neighborhood of periodic motions of an autonomous Hamiltonian system with two degrees of freedom. The problem of the orbital stability of pendulum-like oscillations of a heavy rigid body with a fixed point in the Bobylev – Steklov case is discussed as an application. The nonlinear analysis of orbital stability is carried out including terms through degree six in the expansion of the Hamiltonian function in a neighborhood of the unperturbed periodic motion. This makes it possible to draw rigorous conclusions on orbital stability for the parameter values corresponding to degeneracy of terms of degree four in the normal form of the Hamiltonian function of equations of perturbed motion.

Investigation of the stability of periodic motions in a nonlinear automatic control system based on the fast fourier transform

2003 ◽  
Vol 3 ◽  
pp. 297-307
Author(s):  
V.V. Denisov
Keyword(s):  
Fourier Transform ◽  
Control System ◽  
Automatic Control ◽  
Fast Fourier Transform ◽  
Automatic Control System ◽  
Resonance Phenomenon ◽  
Periodic Motions ◽  
Multiply Connected ◽  
Non Linear ◽  
The Stability

An approach to the study of the stability of non-linear multiply connected systems of automatic control by means of a fast Fourier transform and the resonance phenomenon is considered.

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