Related papers: Numerical-analytical Algorithm for Constructing th…
The paper is devoted to the motion of a body in a fluid under the influence of gravity and drag. Depending on the regime considered, the drag force can exhibit a linear, quadratic or even more general dependence on the velocity of the body…
H${\acute{e}}$non [8] used an inclined billiard to investigate aspects of chaotic scattering which occur in satellite encounters and in other situations. His model consisted of a piecewise mapping which described the motion of a point…
There has been a recent revolution in the ability to manipulate micrometer-sized objects on surfaces patterned by traps or obstacles of controllable configurations and shapes. One application of this technology is to separate particles…
For a polynomial dynamical system, we study the problem of computing the minimal differential equation satisfied by a chosen coordinate (in other words, projecting the system on the coordinate). This problem can be viewed as a special case…
When a solid projectile impacts a granular target, it experiences a drag force and abruptly comes to rest as its momentum transfers to the grains. An empirical drag force law successfully describes the force experienced by the projectile,…
We investigate the qualitative characteristics of a test particle attracted to an irregular elongated body, modeled as a non-homogeneous straight segment with a variable linear density. By deriving the potential function in closed form, we…
The formalism to describe the scattering of a weakly bound projectile nucleus by a heavy target is investigated, using the Uncorrelated Scattering Approximation. The main assumption involved is to neglect the correlation between the…
The vertical trajectory optimization for the en route descent phase is studied in the presence of both along track and cross winds, which are both modeled as functions of altitude. The flight range covers some portion of a cruise segment…
We present a novel numerical method to calculate periodic orbits for dynamical systems by an iterative process which is based directly on the action integral in classical mechanics. New solutions are obtained for the planar motion of three…
We study a pursuit-evasion problem which can be viewed as an extension of the keep-away game. In the game, pursuer(s) will attempt to intersect or catch the evader, while the evader can visit a fixed set of locations, which we denote as the…
Closed form solutions for the computation of the solid angle from polygonal cross-sections are well known, however similar formulae for computation of projected solid angle are not generally available. Formulae for computing the projected…
Recent progress in the simulation of Casimir forces between various objects has allowed traditional computational electromagnetic solvers to be used to find Casimir forces in arbitrary three-dimensional objects. The underlying theory to…
In this paper, we present the mechanics and algorithms to compute the set of feasible motions of an object pushed in a plane. This set is known as the motion cone and was previously described for non-prehensile manipulation tasks in the…
This letter presents a versatile trajectory planning pipeline for aerial tracking. The proposed tracker is capable of handling various chasing settings such as complex unstructured environments, crowded dynamic obstacles and multiple-target…
Three parameterizations are developed for modeling translational motion of a point mass in atmosphere flight over a central rotating body. Unlike well-known parameterizations such as spherical coordinate parameterizations, where position…
We present the scattering approach which is nowadays the best tool for describing the Casimir force in realistic experimental configurations. After reminders on the simple geometries of 1d space and specular scatterers in 3d space, we…
The specific objective of this paper is to develop a tool that calculates the optimal trajectory of the follower aircraft as it completes a formation rejoin, and then maintains the formation position, defined as a ring of points, until a…
Motion of test particles along rotating curved trajectories is considered. The problem is studied both in the laboratory and the rotating frames of reference. It is assumed that the system rotates with the constant angular velocity $\omega…
A little known property of free-fall motion is the elliptic locus of the maximum heights attained by coplanar projectiles launched from a single point in different directions with the same initial speed. Another, less known and perhaps…
We consider an autonomous navigation problem, whereby a traveler aims at traversing an environment in which an adversary tries to set an ambush. A two players zero sum game is introduced. Players' strategies are computed as random path…