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