Related papers: Throwing a Ball as Far as Possible, Revisited
Optimum projection angles for achieving maximum horizontal range in throwing and jumping events are considerably less than 45 degrees. This unexpected result arise because an athlete can generate a greater projection velocity at low…
The problem of determining the angle at which a point mass launched from ground level with a given speed is a standard exercise in mechanics. Similar, yet conceptually and calculationally more difficult problems have been suggested to…
We present an analytical solution for the projectile coplanar motion under constant drag parametrised by the velocity angle. We found the locus formed by the apices of the projectile trajectories. The range and time of flight are obtained…
A classic problem of the motion of a point mass (projectile) thrown at an angle to the horizon is reviewed. The air drag force is taken into account with the drag factor assumed to be constant. Analytic approach is used for investigation.…
A convenient change of variables in the problem of maximizing the horizontal range of the projectile motion, with an arbitrary initial vertical position of the projectile, provides a simple, straightforward solution.
Both null and timelike rays experience trajectory bending in a gravitational field. In this work, we systematically develop a perturbative method to compute the deflection angle of rays with general velocity $v$ in arbitrary static and…
We present an optimal gradient method for smooth strongly convex optimization. The method is optimal in the sense that its worst-case bound on the distance to an optimal point exactly matches the lower bound on the oracle complexity for the…
We consider three problems of selecting optimal gun barrel direction (or those of selecting optimal semiaxis position) when firing an unguided artillery projectile on the assumption that the gun barrel semiaxis can move in a connected…
The image of a point situated at the center of a circularly symmetric potential is a perfect circle. The perturbative effect of non-symmetrical potential terms is to displace and break the perfect circle. These 2 effects, displacement and…
Consider a general nonlinear optimal control problem in finite dimension, with constant state and/or control delays. By the Pontryagin Maximum Principle, any optimal trajectory is the projection of a Pontryagin extremal. We establish that,…
The azimuthal decorrelation between a vector boson and a jet is an essential hard probe in high energy proton-proton and heavy-ion collisions. We overcome intrinsic limitations of previous studies by using a recoil-free axis, achieving…
Accuracy of throwing in games and sports is governed by how errors at projectile release are propagated by flight dynamics. To address the question of what governs the choice of throwing strategy, we use a simple model of throwing with an…
The optimal one-sided parametric polynomial approximants of a circular arc are considered. More precisely, the approximant must be entirely in or out of the underlying circle of an arc. The natural restriction to an arc's approximants…
We investigate variants of Goddard's problems for nonvertical trajectories. The control is the thrust force, and the objective is to maximize a certain final cost, typically, the final mass. In this report, performing an analysis based on…
We present a proof-of-concept study of a method to estimate the inclination angle of compact high velocity clouds (CHVCs), i.e. the angle between a CHVC's trajectory and the line-of-sight. The inclination angle is derived from the CHVC's…
We investigate a limit value of an optimal control problem when the horizon converges to infinity. For this aim, we suppose suitable nonexpansive-like assumptions which does not imply that the limit is independent of the initial state as it…
A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. Air resistance force is taken into account. The quadratic law for the resistance force is used. An analytic approach applies for the…
An investigation on stochastic deflection of high-energy negatively charged particles in a bent crystal was carried out. On the basis of analytical calculation and numerical simulation it was shown that it exists a maximum angle at which…
Let G be a graph that may be drawn in the plane in such a way that all internal faces are centrally symmetric convex polygons. We show how to find a drawing of this type that maximizes the angular resolution of the drawing, the minimum…
I consider a stochastic optimization problem for a time-changed Bessel process whose diffusion rate is constrained to be between two positive values $r_{1}<r_{2}$. The problem is to find an optimal adapted strategy for the choice of…