Based on the modified Landau-Lifshitz-Gilbert equation for an arbitrary Stoner particle under an external magnetic field and a spin-polarized electric current, differential equations for the optimal reversal trajectory, along which the magnetization reversal is the fastest one among all possible reversal routes, are obtained. We show that this is a Euler-Lagrange problem with constrains. The Eu...

Vibration is one of the most important resources of error in motion of tip of flexible robot manipulators. Although much work has been done in the design of controllers for flexible manipulators to follow a specified tip trajectory, it has been done a little work in trajectory planning itself. For redundant robot manipulators, trajectory planning can be accomplished with the aim of optimizing s...

Local Shannon entropy lies at the heart of modern thermodynamics, with much discussion of trajectory-dependent entropy production. When taken at both boundaries of a process in phase space, it reproduces the second law of thermodynamics over a finite time interval for small scale systems. However, given that entropy is an ensemble property, it has never been clear how one can assign such a quan...

Trajectory search for multi-locations in a network is to find the trajectories from the historical dataset such that they can connect the given locations in the network. Existed research mainly focused on the Euclidean space, while in many cases, the track of moving object is often closely related with road networks, and it’s restricted by road networks. In order to obtain an efficient query al...

Abstract. In this paper, the minimum time feedrate trajectory planning problem for five-axis computer numerical control (CNC) machining is studied. A more accurate model for the feedrate trajectory planning problem is proposed by constraining the velocity, acceleration, and jerk for all five axes in the joint space and constraining the chord error in the workpiece coordinate system. For the new...

Linear Dynamidly Varying (LDV) control is a technique for getting a natural (nonlinear, possibly chaotic) trajectory and a perturbed trajectory asymptotically synchroni7ed given an initial condition offset. Probably the best illustrative example, which motivates this paper, is tracking the natural (possibly quasi-periodic) molion of a Tkojan asteroid near the IA point of Jupiter with a spacecra...

The ability to perform tasks similarly to how a specific human would perform them is valuable in future automation efforts across several areas. This paper presents a k-nearest neighbor trajectory generation methodology that creates trajectories similar to those of a given user in the Space Navigator environment using cluster-based player modeling. This method improves on past efforts by genera...

In this paper a closing lemma for C1 nonsingular endomorphisms equivariant under free actions of finite-groups is proved. Hence a recurrent trajectory, as well as all of its symmetric conjugates, of a C1 nonsingular endomorphism equivariant under a free action of a finite group can be closed up simultaneously by an arbitrarily small C1 equivariant perturbation.