Related papers: Maximum range of a projectile thrown from constant…
Based on fundamental properties of light scattering by a particle we reveal the existence of the ultimate upper limit for the light absorption by any partial mode. First, we obtain this result for scattering of a plane wave by a symmetric…
The metric of spherically symmetric ball of ideal liquid is considered in $G^2$- approximation with the help of theory of sources. Using the integral equations of this theory gives the exterior metric depending upon the radius of the ball…
The article discusses the steady motion of a rigid disk of finite thickness rolling on its edge on a horizontal plane under the influence of gravity. The governing equations are presented and two cases allowing for a steady state solution…
We investigated how a target's porosity affects the outcome of a collision, with respect to the impactor's fate. Laboratory impact experiments using peridot projectiles were performed at a speed range between 0.3 and 3.0 km/s, onto high…
The energy-time uncertainty relation puts a fundamental limit on the precision of radars and lidars for the estimation of range and velocity. The precision in the estimation of the range (through the time of arrival) and the velocity…
We study the maximum of a Brownian motion with a parabolic drift; this is a random variable that often occurs as a limit of the maximum of discrete processes whose expectations have a maximum at an interior point. We give series expansions…
A new approach to determining the solar galactocentric distance, $R_0$, from the geometry of spiral-arm segments is proposed. Geometric aspects of the problem are analyzed and a simplified three-point method for estimating $R_0$ from…
We investigate whether a robot arm can learn to pick and throw arbitrary objects into selected boxes quickly and accurately. Throwing has the potential to increase the physical reachability and picking speed of a robot arm. However,…
The study of rational point sets on circles over the Euclidean plane is discussed in a more general framework, i.e. we generalize the notion rational and consider these circular point sets over arbitrary fields. We also determine the…
The equations of motion are solved analytically for speed and position for the case of blackbody friction on objects traveling at relativistic speeds with respect to observers fixed in the frame of the blackbody radiation. Two model cases…
The aerodynamics of a projectile launched from barrels of various devices is quite complicated due to its interactions with the unsteady flow field around it. A computational study using moving grid method is performed here to analyze the…
In this paper we study the problem of maximizing the distance to a given point over an intersection of balls. It was already known that this problem can be solved in polynomial time and space if the given point is not in the convex hull of…
We investigate theoretically the ballistic motion of small legged insects and legless larvae after a jump. Notwithstanding their completely different morphologies and jumping strategies, these legged and legless animals have convergently…
It is a common phenomenon in nature and technology that a system under perturbations exits a regime of its usual dynamics. Often it is possible to define a potential function whereby a potential well can be associated with a usual or…
Why do curling stones curl? That is a question physicists are often asked, yet no answer has been established. Stones rotating clockwise curl right, contrary to our naive expectations. After a century of debate between contradicting…
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
We consider the simplest case of Rutherford scattering, i.e. the head-on collision, where the projectile is treated quantum mechanically. The convexity of repulsive Coulomb force invokes a disagreement between the Ehrenfest's and Hamilton's…
In this article, we study the behaviour of a looped string launched in ambient air using motorised wheels. We show that the loop, once it reaches its stationary state, is either in the pulley or the air-lifted state. The transition between…
The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential…
We discuss a trajectory of penguins' faeces after the powerful shooting due to their strong rectal pressure. Practically, it is important to see how far faeceses reach when penguins expel them from higher places. Such information is useful…