Delay-distribution based stability analysis of time-delayed port-Hamiltonian systems

2012 ◽  
Author(s):  
Pankaj Mukhija ◽  
I. N. Kar ◽  
R. K. P. Bhatt
Keyword(s):  
Stability Analysis ◽  
Hamiltonian Systems ◽  
Delay Distribution

scholarly journals Is there a Connection between Local and Global (In-)Stability?

1986 ◽  
Vol 39 (3) ◽  
pp. 331 ◽  
Author(s):  
B Eckhardt ◽  
JA Louw ◽  
W-H Steeb
Keyword(s):  
Stability Analysis ◽  
Hamiltonian Systems ◽  
Local Stability ◽  
Large Scale ◽  
Equations Of Motion ◽  
Riemannian Curvature ◽  
Local Stability Analysis

We review two criteria which have been used to predict the onset of large scale stochasticity in Hamiltonian systems. We show that one of them, due to Toda and based on a local stability analysis of the equations of motion, is inconclusive. An approach based on the local Riemannian curvature K of trajectories correctly predicts chaos if K < 0 everywhere, but�no further conclusions can be drawn. New (counter-)examples are provided.

Linear stability analysis of the figure-eight orbit in the three-body problem

2007 ◽  
Vol 27 (6) ◽  
pp. 1947-1963 ◽  
Author(s):  
GARETH E. ROBERTS
Keyword(s):  
Stability Analysis ◽  
Hamiltonian Systems ◽  
Linear Stability Analysis ◽  
Body Problem ◽  
Monodromy Matrix ◽  
Three Body Problem ◽  
Wide Range ◽  
Linear Differential ◽  
Three Body ◽  
Characteristic Multipliers

AbstractWe show that the well-known figure-eight orbit of the three-body problem is linearly stable. Building on the strong amount of symmetry present, the monodromy matrix for the figure-eight is factored so that its stability can be determined from the first twelfth of the orbit. Using a clever change of coordinates, the problem is then reduced to a 2×2 matrix whose entries depend on solutions of the associated linear differential system. These entries are estimated rigorously using only a few steps of a Runge–Kutta–Fehlberg algorithm. From this, we conclude that the characteristic multipliers are distinct and lie on the unit circle. The methods and results presented are applicable to a wide range of Hamiltonian systems containing symmetric periodic solutions.

Sign in / Sign up

Export Citation Format

Share Document