Related papers: Maximum range of a projectile thrown from constant…
In contrast to set-point tracking which aims to reduce the tracking error between the tracker and the reference, tracking-in-range problems only focus on whether the tracker is within a given range around the reference, making it more…
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…
Suppose a projectile collides perpendicularly with a stationary rigid rod on a smooth horizontal table. We show that, contrary to what one naturally expects, it is not always the case that the rod acquires maximum angular velocity when…
The inner movement of a trebuchet with swinging counterweight was measured inside a laboratory by the use of rotation sensors to determine angular coordinates for beam, counterweight and sling. Data collection was started before the…
Model rockets have been employed in student projects, but very few papers in aerospace education offer concise summaries of activities at university-course levels. This paper aims to address this gap in the literature. The rockets used by…
A two-dimensional body moves through a rarefied medium; the collisions of the medium particles with the body are absolutely elastic. The body performs both translational and slow rotational motion. It is required to select the body, from a…
Interaction of spin with electromagnetic field yields an effective metric along the world line of spinning particle. If we insist to preserve the usual special-relativity definitions of time and distance, critical speed which spinning…
How to distribute a set of points uniformly on a spherical surface is a very old problem that still lacks a definite answer. In this work, we introduce a physical measure of uniformity based on the distribution of distances between points,…
We apply a new notion of angle between projections to deduce criteria for uniform convergence results of the alternating projections method under several different settings: averaged projections, cyclic products, quasi-periodic products and…
We consider the precise upper large deviations estimates for the maximal displacement of a branching random walk. In addition, we obtain a description of the extremal process of the branching random walk conditioned on this large deviations…
The effectiveness of a robot manipulation to a large extent is determined by the speed of making this or that movement needed for carrying out the task. Accordingly to this the problem of optimal robot control is often subdivided into two…
In this paper we study the NP-Hard problem of maximizing the distance over an intersection of balls to a given point. We expand the results found in \cite{funcos1}, where the authors characterize the farthest in an intersection of balls…
New measurements are presented of the lift on a spinning baseball. The experiment utilizes a pitching machine to project the baseball horizontally; a high-speed motion capture system to measure the initial velocity and angular velocity and…
The ball-constrained weighted maximin dispersion problem $(\rm P_{ball})$ is to find a point in an $n$-dimensional Euclidean ball such that the minimum of the weighted Euclidean distance from given $m$ points is maximized. We propose a new…
Motivated by the problem of computing the distribution of the largest distance $d_{\max}$ between $n$ random points on a circle we derive an explicit formula for the moments of the maximal component of a random vector following a Dirichlet…
In the present paper, the trace distance is exposed within the quantum operations formalism. The definition of the trace distance in terms of a maximum over all quantum operations is given. It is shown that for any pair of different states,…
The maximum size of a cosmic structure is given by the maximum turnaround radius -- the scale where the attraction due to its mass is balanced by the repulsion due to dark energy. We derive generic formulae for the estimation of the maximum…
We measure ejecta mass as a function of azimuthal and impact angle for 104 m/s oblique impacts into sand. We find that the ejecta mass distribution is strongly sensitive to azimuthal angle with as high as 8 times more mass in ejecta on the…
The isoperimetric problem asks for the maximum area of a region of given perimeter. It is natural to consider other measurements of a region, such as the diameter and width, and ask for the extreme value of one when another is fixed. The…
We consider a square expanding with constant speed seen from an observer moving away with constant acceleration and study the distribution of angles between rays from the observer towards the lattice points in the square. We prove the…