On the stability of equilibria of Hamiltonian systems near the main resonances

1984 ◽  
Vol 33 (2) ◽  
pp. 159-167 ◽  
Author(s):  
E. E. Shnol
Keyword(s):  
Hamiltonian Systems ◽  
Stability Of Equilibria ◽  
The Stability

ON 3D HAMILTONIAN SYSTEMS VIA DARBOUX–WEINSTEIN COORDINATES

2009 ◽  
Vol 06 (03) ◽  
pp. 451-459
Author(s):  
RĂZVAN M. TUDORAN ◽  
RAMONA A. TUDORAN
Keyword(s):  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Three Dimensional ◽  
Stability Of Equilibria ◽  
Existence Of Periodic Solutions ◽  
The Stability

In this paper we are analyzing the stability of equilibria and also the existence of periodic solutions of three dimensional Hamiltonian systems using Darboux–Weinstein coordinates.

Stabilizing Feedback Controls for Nonlinear Hamiltonian Systems and Nonconservative Bilinear Systems in Elasticity

1982 ◽  
Vol 104 (1) ◽  
pp. 27-32 ◽  
Author(s):  
S. N. Singh
Keyword(s):  
Asymptotic Stability ◽  
Hamiltonian Systems ◽  
Attitude Control ◽  
Sufficient Conditions ◽  
Bilinear Systems ◽  
Feedback Controls ◽  
Control Laws ◽  
Nonlinear Maps ◽  
The Stability ◽  
Necessary And Sufficient

Using the invariance principle of LaSalle [1], sufficient conditions for the existence of linear and nonlinear control laws for local and global asymptotic stability of nonlinear Hamiltonian systems are derived. An instability theorem is also presented which identifies the control laws from the given class which cannot achieve asymptotic stability. Some of the stability results are based on certain results for the univalence of nonlinear maps. A similar approach for the stabilization of bilinear systems which include nonconservative systems in elasticity is used and a necessary and sufficient condition for stabilization is obtained. An application to attitude control of a gyrostat Satellite is presented.

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