Randomized system trajectories

Array P System with Shuffle on Trajectories

In this paper, we introduce a new concept of trajectory array P system which consists of a membrane structure in which the objects are arrays and the evolutionary rules are given in terms of trajectories. We present some properties of trajectory array P system and compare with certain families of picture languages. We consider a variant of trajectory array P system and show that the languages g...

Thrust - Limited Optimal Three - Dimensional Spacecraft Trajectories

Several optimal three-dimensional orbital transfer problems are solved for thrust-limited spacecrafts using collocation and nonlinear programming techniques. The solutions for full nonlinear equations of motion are obtained where the integrals of the free Keplerian motion in three dimensions are utilized for coasting arcs. In order to limit the solution space, interior-point constraints are use...

Trajectories 449 Dynamical Trajectories and Curvature Trajectories

Pseudo Closed Trajectories in the Family of Trajectories Defined by a System of Differential Equations

Some of these curves are considered in a rather incidental way in the writings of Poincare.** However, the full concept of pseudo closed trajectories does not seem to have been discussed explicitly heretofore. We assume that all of the variables in the equations (1) are real, that the functions X and Y are continuous in an open connected region R in the xy-plane, that these functions satisfy Li...

Convergence of trajectories in infinite horizon optimization

In this paper, we investigate the convergence of a sequence of minimizing trajectories in infinite horizon optimization problems. The convergence is considered in the sense of ideals and their particular case called the statistical convergence. The optimality is defined as a total cost over the infinite horizon.