Gradient Trajectories For Plane Singular Metrics I: Oscillating Trajectories

Oscillating Radial Trajectories for Reduced Undersampling Artifacts

Introduction: In this work, we propose an oscillating radial sampling of k-space which shows a significant improvement in the reconstruction quality over the traditional radial sampling based reconstruction. The incoherency in spatial aliasing artifacts is selected as a criterion for optimizing the k-space trajectory. Adding oscillations reduces the coherency in the k-space trajectory and hence...

Singular Trajectories of Control-Affine Systems

When applying methods of optimal control to motion planning or stabilization problems, some theoretical or numerical difficulties may arise, due to the presence of specific trajectories, namely, singular minimizing trajectories of the underlying optimal control problem. In this article, we provide characterizations for singular trajectories of control-affine systems. We prove that, under generi...

Biomechanical Investigation of Empirical Optimal Trajectories Introduced for Snatch Weightlifting

The optimal barbell trajectory for snatch weightlifting has been achieved empirically by several researchers. They have studied the differences between the elite weightlifters’ movement patterns and suggested three optimal barbell trajectories (type A, B, and C). But they didn’t agree for introducing the best trajectory. One of the reasons is this idea that the selected criterion by researchers...

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