Median Trajectories

Handling Inharmonic Series with Median-adjustive Trajectories

A new method for the analysis of inharmonic instrumental tones is presented. The method exploits an equation derived from the well-know inharmonic series equation, where the inharmonicity coefficient is balanced with the frequencies and numbers of any two partials extracted from a pseudo-harmonic series. A serial search for increasingly deviating spectral peaks is aided with the integrated refi...

On Median Graphs and Median Grid Graphs on Median Graphs and Median Grid Graphs

Let e be an edge of a median graph G which is contained in exactly one 4-cycle. Then it is proved that G n e is a median graph. The converse holds as well provided that e is not contained is a subgraph isomorphic to the 3-cube minus a vertex. These results are used to give several characterizations of median grid graphs. (Grid graphs are subgraphs of complete grids, i.e. of the Cartesian produc...

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

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.