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This paper describes a novel and fast, simple and robust algorithm with O(N) expected complexity which enables to decrease run time needed to find the maximum distance of two points in E2. It can be easily modified for the E3 case in…
Motion of a point particle sliding on a turntable is studied. The equations of motion are derived assuming that the table exerts frictional force on the particle, which is of constant magnitude and directed opposite to the direction of…
The goal of this paper is to investigate the normal and tangential forces acting at the point of contact between a horizontal surface and a rolling ball actuated by internal point masses moving in the ball's frame of reference. The normal…
We discuss the problem of how to calculate the distance between two cosmological objects given their redshifts and angular separation on the sky. Although of a fundamental nature, this problem and its solution seem to lack a detailed…
Railguns are capable to far exceed the muzzle energies of current naval deck guns. Therefore one of the most promising scenario for the future application of railguns in naval warfare is the long range artillery. Hypervelocity projectiles…
We analyze the motion of a rod floating in a weightless environment in space when a force is applied at some point on the rod in a direction perpendicular to its length. If the force applied is at the centre of mass, then the rod gets a…
Rapidly generating an optimal chasing motion of a drone to follow a dynamic target among obstacles is challenging due to numerical issues rising from multiple conflicting objectives and non-convex constraints. This study proposes to resolve…
We consider many-body problems in classical mechanics where a wide range of time scales limits what can be computed. We apply the method of optimal prediction to obtain equations which are easier to solve numerically. We demonstrate by…
Methods are presented for measuring thrust using common force sensors and data acquisition to construct a dynamic force plate. A spreadsheet can be used to compute trajectory by integrating the equations of motion numerically. These…
Accuracy levels of metres per second require the fundamental concept of 'radial velocity' for stars and other distant objects to be examined, both as a physical velocity, and as measured by spectroscopic and astrometric techniques. Aiming…
This paper studies the problem of identifying directions of axial symmetry in multivariate distributions. Theoretical results are derived on how the measure or cardinality of the set of symmetry directions relates to spherical symmetry. The…
In many robotics applications, it is necessary to compute not only the distance between the robot and the environment, but also its derivative - for example, when using control barrier functions. However, since the traditional Euclidean…
This article describes four innovative pedagogical exercises: (i) The expression for relation between cross sections in the laboratory and the centre of mass systems provided in text books assumes zero or low Q values which needs to be…
In this article, we study the maximal displacement of critical branching random walk in random environment. Let $M_n$ be the maximal displacement of a particle in generation $n$, and $Z_n$ be the total population in generation $n$, $M$ be…
We propose a new method to construct maximin distance designs with arbitrary number of dimensions and points. The proposed designs hold interleaved-layer structures and are by far the best maximin distance designs in four or more…
Problems involving rotating systems analyzed from an inertial frame, without invoking fictitious forces, is something that freshman students find difficult to understand in an introductory mechanics course. One of the problems that I…
The aim of the present article is to give an exact and correct representation of the essentially important part of modern special relativity theory that touches upon the behavior of the proper length of accelerated moving bodies.In…
In the event of a total loss of thrust, a pilot must identify a reachable landing site and subsequently execute a forced landing. To do so, they must estimate which region on the ground can be reached safely in gliding flight. We call this…
We obtain a polynomial upper bound on the mixing time $T_{CHR}(\epsilon)$ of the coordinate Hit-and-Run random walk on an $n-$dimensional convex body, where $T_{CHR}(\epsilon)$ is the number of steps needed in order to reach within…
The musculoskeletal humanoid has various biomimetic benefits, and the redundant muscle arrangement is one of its most important characteristics. This redundancy can achieve fail-safe redundant actuation and variable stiffness control.…