54 research outputs found
Interplay of linear and nonlinear impurities in the formation of stationary localized states
Formation of stationary localized states in one-dimensional chain as well as
in a Cayley tree due to a linear impurity and a nonlinear impurity is studied.
Furthermore, a one-dimensional chain with linear and nonlinear site energies at
the alternate sites is studied and rich phase diagrams of SL states are
obtained for all systems we considered. The results are compared with those of
the linear and nonlinear systems.Comment: 7 pages, Latex, 7 figure
Trajectory optimization by a direct descent process
The problem considered is that of trajectory optimization using step-by-step descent to minimum cost along the direction of the cost gradient with respect to the control. Using a hybrid computer, the gradient is computed di rectly as the response to nearly impulsive control perturba tions. A method is presented for computing the gradient when several terminal constraints are enforced. Examples of application of the method are presented. It is concluded that the direct gradient computation method has some significant advantages over other methods.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68738/2/10.1177_003754976801100308.pd
Energy levels of periodic solutions of the circular 2+2 Sitnikov problem
We study a 2+2 body problem introduced in a previous paper as the circular
double Sitnikov problem. Since the secondary bodies are moving on the same
perpendicular line where evolve the primaries, almost every solution is a
collision orbit. We extend the solutions beyond collisions with a symplectic
regularization and study the set of energy surfaces that contain periodic
orbits and their foliations .Comment: 20 pages, 5 figures. This is not the final version
Analysis and synthesis of oscillator systems described by perturbed single well Duffing equations
Identifying and Quantifying Mis-Modeled Dynamics via Optimal Control Problem Distance Metrics
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